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THE NATURE OF CAPITAL AND INCOME 



-y^)^' 



THE NATURE OF CAPITAL 
AND INCOME 



BY 
IRVING FISHER, Ph.D. 

PBOFESSOE OF POLITICAL ECONOMY, TALE UNIVERSITT 



THE MACMILLAN COMPANY 

LONDON: MACMILLAN & CO., Ltd. 

1906 

All rights reserved 



II 1906 




OOPYB 



HB4o ( 



COPYEIGHT, 1906, 

bt the macmillan company. 



Set up and electrotyped. Published September, 1906. 



ITortoaotr ^ress 

J. S. Gushing & Co. — Berwick & Smith Co. 

Norwood, Mass., U.S.A. 



TO 

WILLIAM GRAHAM SUMNER 

WHO FIRST INSPIRED ME 

WITH 

A LOVE FOR 

ECONOMIC SCIENCE 



PREFACE 

This book is an attempt to put on a rational foundation 
the concepts and fundamental theorems of capital and 
income. It therefore forms a sort of philosophy of eco- 
nomic accounting, and, it is hoped, may supply a link long 
missing between the ideas and usages underlying prac- 
tical business transactions and the theories of abstract 
economics. To some readers it may seem that certain 
elementary topics have been treated at undue length ; but, 
as experience shows that economic structures built on 
hasty and inadequate generalizations inevitably collapse, 
it seems hardly possible to take too much pains in making 
the foundations secure. On the other hand, topics which 
are in their nature technical or which digress from the 
main theme — and in particular mathematical formulae — 
have been relegated to appendices. 

Many of the theses maintained will undoubtedly fail 
to command assent on a first reading, for in any orderly 
presentation of a subject it is impossible to forestall all 
objections as they occur. The aim has been to pre- 
serve a definite sequence by which each step prepares 
the way for those which follow; but this plan has ne- 
cessitated the postponement of some topics beyond the 
point at which a consciousness of their difficulties 
might begin to trouble the reader. He is therefore 
asked to stay judgment until he has finished the work, 
and, if necessary, to reread those parts in which his diffi- 
culties were first encountered. This suggestion is espe- 
cially urged in regard to the treatment of income, the 
concept of which forms the central theme of the book. 
Many of the friendly critics to whom the manuscript has 



viii PREFACE 

been shown have at first dissented strongly from the con- 
clusions of Chapter VII, but have invariably withdrawn 
their objections after finishing Chapter XIV. 

The nature of income is a subject which has not hitherto 
received, in economic literature, the attention it deserves. 
Income plays an important role in all economic problems ; 
it is income for which capital exists ; it is income for which 
labor is exerted ; and it is the distribution of income which 
constitutes the disparity between rich and poor. 

Nor is the subject of interest solely to theoretical econo- 
mists. It appeals to practical men of affairs and to those 
who are interested in problems of social reform, as well as 
to the special classes of accountants, actuaries, and mathe- 
maticians. The book is so arranged that the general 
reader may, if he so desires, omit the technical por- 
tions, such as the appendices and possibly Chapter XVII. 
It is suggested that all readers should give special atten- 
tion to Chapters VI, VII, IX, and XIV. 

The problem of nomenclature has proved not a little 
puzzling. In general, each term has been employed in 
one, and only one, sense ; but to follow this plan exclu- 
sively has not been found practicable. Several words are 
sometimes used for the same concept, — for instance, "re- 
sources" and "assets," or "utility "and "desirability"; and 
sometimes the same word has been used in more than one 
sense, as in the case of " capital," which may mean capital- 
goods or capital- value. But special pains have been taken 
to avoid any confusion or uncertainty of meaning. The 
definitions have been carefully framed, and will be found 
collected in a glossary at the end. 

A few fragments of the book have appeared in a some- 
what different form in economic periodicals, and the 
whole book may be said to be only the elaboration of the 
ideas outlined some years ago in the Economic Journal. 
I would express my thanks to the publishers of the 
Economic Journal for permission to use unaltered some 



PREFACE ix 

passages from " What is Capital ? " 1897, " Senses of 
Capital," 1898, and " The Role of Capital in Economic 
Theory," 1898, and to the Quarterly Journal of Economics 
for similar permission with reference to "Precedents for 
Defining Capital," 1904. 

I wish also to express my obligations to the many 
persons who have aided me in the preparation of this 
work, among them especially my wife ; my brother, Mr. 
Herbert W. Fisher ; my colleagues. Professor Henry C. 
Emery, Professor John P. Norton, and Dr. Lester W. 
Zartman; and my friends, Mr. Richard M. Hurd and 
Mr. Orland S. Isbell of New York City. 

IRVING FISHER. 
New Haven, Conn., June, 1906. 



CONTENTS 

FIRST SUMMARY 

OHAPTEKS 

INTEODUCTION. FUNDAMENTAL CONCEPTS . . I-III 

PART I. CAPITAL IV-VI 

PART II. INCOME . VII-X 

PART III. CAPITAL AND INCOME .... XI-XVI 
PART IV. SUMMARIES XVII-XVIII 



xu 



CONTENTS 



SECOND SUMMARY 
INTRODUCTION 

OHAFTEB FAeS 

I. Wealth .......... 3 

II. Propbrtt 18 

III. Utility 41 

PART I 

IV. Capital 51 

V. Capital Accounts 66 

VI. Capital Summation 90 

PART II 

VII. Income 101 

VIII. Income Accounts 119 

IX. Income Summation . . . 141 

X. Psychic Income 165 



PART III 

XL Four Income-capital Ratios . 

XII. Concept of Rate of Interest 

XIII. Value of Capital . 

XIV. Earnings and Income 

XV. Capital and Income Accounts 

XVI. The Risk Element . 



183 
191 
202 
227 
256 
265 



PART IV 

XVII. Summary of Part III 303 

XVIIL General Summary ........ 323 

Glossary. Summary of Definitions 329 

APPENDICES 341 

INDEX 413 



ANALYTICAL TABLE OF CONTENTS 



CHAPTER I 



Wealth 

§ 1. Definition of wealth 

§ 2. Classification of wealth . 

§ 3. Measurement of wealth . 

§ 4. Price of wealth 

§ 5. Market-, asking-, appraised-price 

§ 6, Value of wealth 

§ 7. Quantity, price, and value contrasted 

§ 8. Accuracy in measurement of quantity, price, and value 



3 

5 
8 
9 
11 
13 
14 
15 



CHAPTER II 



Pkopekty 

§ 1. Definition of property 

§ 2. Definition of services 

§ 3. Definition of rights . 

§ 4. Wealth and property correlative 

§ 5. Table illustrating this correlation 

§ 6. A guide for finding wealth underlying given property rights 

§ 7. A second guide : One property right overlaid by another 

§ 8. A third guide : Property rights are always to existing wealth 

§ 9. Total ownership is aggregate of partial rights . 

§ 10. Classification of property rights . . ... 

§ 11. Importance of a clear understanding of wealth and property 



18 
19 
20 
22 

24 
24 
31 
32 
34 
36 
38 



CHAPTER III 
Utility 

§ 1. Desirability vs. satisfaction 41 

§ 2. Synonyms for desirability (utility, etc.) 42 

§ ;l Desirability vs. services 43 

xiii 



xiv ANALYTICAL TABLE OF CONTENTS 



§ 4. Total and marginal desirability 44 

§ 5. Law of decreasing marginal desirability 46 



CHAPTER rV 
Capital 

§ 1. Pund and flow distinguished. Capital and income . , 51 

§ 2. Discordant definitions of capital 53 

§ 3. Fundamental truths in these conflicting definitions . . 57 

§ 4. Confusions resulting from neglect to introduce time element 58 

§ 5. The weight of economic usage 60 

§ 6. Popular and business usage 61 

§ 7. Correct terminology less important than correct thinking . 65 



CHAPTER V 
Capital Accounts 

§ 1. Senses of capital 66 

§ 2. Book capitalization 68 

§ 3. Book and market values 70 

§ 4. Summary of senses of capital 72 

§5. Case of decreasing capital-balance . . . . . .73 

§ 6. Effect of payments between stockholders and company . . 75 

§7. " Rights to subscribe " 77 

§ 8. Stock watering 79 

§ 9. Insolvency 81 

§ 10. Pseudo-insolvency 82 

§ 11. Creditor nominally takes no risk 82 

§ 12. But practically creditor is risk-taker 84 

§ 13. Winding up a bankrupt company 86 

§ 14. One bankruptcy leads to another 87 

§ 15. Summary 89 



CHAPTER VI 

Capital Summation 

§ 1. Methods of couples and balances 90 

§ 2. Distinction between accounts of real and fictitious persons . 92 
§ 3. Summation by couples brings into relief concrete capital . 93 



^ 



ANALYTICAL TABLE OF CONTENTS xv 

PAOB 

§ 4. Nature of credit 96 

§ 6. Importance of distinguishing methods of couples and balances 97 

CHAPTER VII 

Income 

§ 1. Difficulties of defining income 101 

§ 2. The money-income concept 103 

§ 3. The real-income concept 104 

§ 4. Error of including as income both commodities and services . 106 

§ 5. Vain attempts to escape the pitfalls thus laid .... 109 
§ 6. Income not restricted to " enjoyable " elements . . .112 

§ 7. So-called social and individual income 113 

§ 8. Conclusion 115 

CHAPTER VIII 
Income Accounts 



§ 1. Introduction 119 

§ 2, Specimen income and outgo accounts 121 

§ 3. Cost of construction is to be included in outgo accounts . . 124 

§ 4. Devices for making income regular 127 • 

§ 5. Applications of income accounting 129 

§ 6. Example of individual accounts 131 

§ 7. Income and outgo account for negative capital (liabilities) . 134 

§ 8. Limitations of practical bookkeeping 135 

§ 9. Income accounts for fictitious persons 138 

§ 10. Relation of income accounts to capital accounts . . . 139 

CHAPTER IX 

Income Summation 

§1. Summation by " method of balances " 141 

§2. "Interactions" 143 

§ 3. Interactions which change the form of wealth (production) . 145 

§ 4. Interactions which change the place of wealth (transportation) 148 

§ 5. Interactions which change the ownership of wealth (exchange) 149 

§ 6. Accounts illustrative of the first class (production) . . 152 

§ 7. Results of combining these accounts 156 

§ 8. Methods of balances and couples contrasted .... 157 

§ 9. Accounts illustrative of the third class, for fictitious persons . 158 

§ 10. Accounts illustrative of the third class, for real persons . . 162 

§ 11. Conclusion 164 



XVI 



ANALYTICAL TABLE OF CONTENTS 



CHAPTER X 
Psychic Income 

§ 1. Objective income leads up to subjective . 

§ 2. Illustrative cases 

§ 3. Concept of subjective income .... 

§ 4. Objective and subjective incomes differ in time 

§ 5. Objective and subjective incomes differ as to labor 

§ 6. Labor the only ultimate cost of production 

§ 7. Objective and subjective income differ as to pain 

§ 8. Summary 

§ 9. Classification of services 



PAGE 

165 
165 
167 
169 
170 
173 
175 
177 
178 



CHAPTER XI 
Tour Income-capital Ratios 



§ 1. Besume of previous chapters 183 

§ 2. Physical- and value-productivity, physical- and value-return . 184 

§ 8. Errors from confusing them Ib6 

§ 4. How costs, past and future, affect values 188 : 



CHAPTER XII 
Concept of Rate of Interest — -^ 

§ 1. The rate of interest as a case of " value-return " . . . 191 

§ 2. Annual, semi-annual, quarterly, and continuous reckoning . 192 

§ 3. Rate of capitalization or reciprocal of the rate of interest . 19i 

§ 4. The " premium " and " price " concepts of the rate of interest 194 

§ 5. The conditions under vphich they are interchangeable . . 196 

§ 6. Conditions under vrhich they are not interchangeable . . 198 

§ 7. The rate of discount .199 

§ 8. Summary 199 



CHAPTER XIII 

Value of Capital „ 

§ 1. Capital- value of a single future item. The "discount curve " 

§ 2. Application to valuing capital, property, and wealth 

§ 3. Capital-value of a perpetual annuity 

§ 4. Application to valuing capital, property, and wealth 

§ 5. Capital-value of a terminable annuity 

§ 6. Application to valuing capital, property, and wealth 

§ 7. Capital-value of a bond 

§ 8. Capital-value of any income stream whatever 



202 

204' 

205' 

208 

209 

210 

211 

217 



ANALYTICAL TABLE OF CONTENTS 



XVll 



§ 9. Capital-value when alternative income streams are possible 

§ 10. Capital-value of a group of articles 

§ 11. General conclusion 



PAOE 

221 
223 
223 



CHAPTER XIV 

Earnings and Income 

§ 1. Capital-value less than total anticipated income . . . 227 

§2. Effect of a change in the rate of interest .... 229 

§ 3. Value-return may be greater or less than rate of interest . 229 

§ 4. Standard or earned income vs. realized income . . . 231 

§ 5. Increase of capital equals excess of earnings over income . 236 

§ 6. A depreciation fund as a means of standardizing income . 238 

§ 7. Sinking funds 243 

§ 8. Other devices for making income regular .... 244 

§ 9. The device of keeping a large stock of instruments . . 246 

§ 10. Savings are not a part of realized income .... 247 

§11. Imaginary case of three brothers 249 

§ 12. An ' ' income ' ' tax on the three brothers .... 250 

§ 13. A misconceived income tax affects the use of capital . . 253 

§ 14. To consider " savings " income confuses capital and income . 254 



CHAPTER XV 

Capital and Income Accounts 

§ 1. Capital and income accounts when items recur regularly. 

§ 2. Case in which repairs occur at long intervals . 

§ 3. The same, when there is a repair fund but no repairs as yet 

§ 4. The same, when repairs actually occur .... 

§ 5. Extraordinary increases or decreases .... 

§ 6. Conclusion 



256 
257 
259 
261 
263 
264 



CHAPTER XVI 

The Risk Element 

§ 1. Subjective nature of chance . . , . . 

§ 2. Definition of chance 

§ 3. Risk as applied to the rate of interest .... 

§ 4. Same, in case future income is dependent on rate of interest 

§ 5. Risk as applied to immediate income .... 

§ 6. "Riskless," "mathematical," and "commercial" values 

§ 7. Capital-value of a risky bond 

§ 8. Riskless, mathematical, and commercial rates of interest 

§ 9. Inverse case, where instead of risk of loss there is chance of gain 



265 
269 
271 

273 
275 
276 
277 
279 
280 



xviii ANALYTICAL TABLE OF CONTENTS 

PAGE 

§ 10. The general case, where both are present .... 281 

§ 11. Difficulties in practice 283 

§ 12. Enumeration of causes affecting capital-value . , . 284 

§ 13. Effect of chance on the form of the " discount curve " . . 286 

§ 14. Effect of chance on bookkeeping 287 

§ 15. Five methods of avoiding risk 288 

§ 16. The method of guaranties 288 

§ 17. The method of safeguards 289 

§ 18. The method of increasing knowledge 291 

§ 19. The method of insurance 291 

§ 20. Forms of insurance 294 

§21. Shifting risks to speculators. Dangers of imitative speculations 295 

§ 22. Buying and selling futures 298 

CHAPTER XVII 
Summary of Part III bt Means op Diagrams 



§ 1. Mode of representation adopted 

§ 2. Capital- value as discounted income 

§ 3. Capital-value as mean between past cost and future income 

§ 4. How to combine capital curves 

§ 5. Resultant in case of interactions 

§ 6. Application to summation of capital of individuals . 

§ 7. Application to summation of capital of society 

§ 8. An " interaction " as preparatory to enjoyable services . 

§ 9. The risk element 



CHAPTER XVIII 
General Summary 



§ 1. Picture of capital and income 

§ 2. Summation of capital and income .... 

§ 3. Subjective counterparts of objective capital and income 

§ 4. Relative changes in values of capital and income . 

§ 5. Final summary 



303 

304. 

305- 

309 

311 

314 

316 

317 

320 



323 
324 

326 
327 
328 



GLOSSARY 
Summary of Definitions 329 



APPENDICES 



Appendix to Chapter I 

FAGB 

§ 1 (to Ch. I, § 7). Dimensions of quantity, value, and price of 

wealth 341 

Appendix to Chapter III 

§ 1 (to Ch. Ill, § 4). Mathematical expression for marginal desir- 
ability 344 

Appendix to Chapter VII 
§ 1 (to Ch. VII, § 1). Specimens of current definitions of income . 345 

Appendix to Chapter XI 

§ 1 (to Ch. XI, § 2). Mathematical dimensions of income-capital 

ratios 357 

Appendix to Chapter XII 

§ 1 (to Ch. XII, § 2). Mathematical relations between rates of 
interest reckoned annually, semi-annually, etc., when the rates 
are conceived in the " price " sense 357 

§ 2 (to Ch. XII, § 4). The same, when the interest rates are con- 
ceived in the " premium " sense. Diagrammatic representation. 
Economic interpretation of e 358 

§ 3 (to Ch. XII, § 6). A premium rate of 4 per cent in one year and 
3 per cent thereafter, means a price rate of 3.03 per cent the 
first year and 3 per cent thereafter 362 

§ 4 (to Ch. XII, § 6). A price rate of 4 per cent in one year and 
3 per cent thereafter means a premium rate of 37^ per cent the 
first year and 3 per cent thereafter 362 

§ 5 (to Ch. XII, § 6). Mathematical relations between the rates of 

interest as a premium and as a price 363 

§ 6 (to Ch. XII, § 7) . Mathematical relations between the rates of 

interest and discount 364 

§ 7 (to Ch. XII, § 7). Mathematical relations between rates of dis- 
count for different time reckonings 366 

§ 8 (to Ch. XII, § 8). Dimensions of rates of interest, discount, 

and capitalization 367 



XX ANALYTICAL TABLE OF CONTENTS 

Appendix to Chapter XIII 

PAGE 

§ 1 (to Ch. XIII, § 1). Formula for capital-value of a sum due in 
one year ........... 368 

§ 2 (to Ch. XIII, § 1). Formula for capital-value of a sum F, due 
at end of any time t 368 

§ 3 (to Ch. XIII, § 3). Formula for capital- value of a perpetual 

annuity 369 

§ 4 (to Ch. XIII, § 3). Formulae and diagrams for capital- value of 
annuities payable annually, semi-annually, quarterly, and con- 
tinuously 369 

§ 5 (to Ch. XIII, § 3). Diagrams for discontinuous and continu- 
ous income 371 

§ 6 (to Ch. XIII, § 5). Formula for capital- value of a terminable 

annuity 374 

§ 7 (to Ch. XIII, § 5). Discussion of formulae for terminable 

annuities by diagrams. "Total discount." " Total interest " 374 
§ 8 (to Ch. XIII, § 7). Formula} for value of bond . . .378 
§ 9 (to Ch. XIII, § 7). Alternative method for computing value 
of a bond 380 

§ 10 (to Ch. XIII, § 7). Formula for a bond -when interest is 

reckoned oftener than yearly 382 

§ 11 (to Ch. XIII, § 8). Formula for capital-value of any series of 

income installments 382 

§ 12 (to Ch. XIII, § 8). Diagram and formula for deriving capital- 
value from a given continuous income stream .... 383 

§ 13 (to Ch. XIII, § 8). Diagram showing the accumulated 

"amount" of a given income stream 387 

§ 14 (to Ch. XIII, § 10). Effect of reckoning semi-annually, quar- 
terly, and continuously, on the rate of interest realized from 
the income of a continuously replenished stock of articles . . 388 

§ 15 (to Ch. XIII, § 11). Influence of variation in the rate of 

interest . 390 

§ 16 (to Ch. XIII, § 11). Kepresentation of capital and income by 

polar coordinates . • 393 



Appendix to Chapter XIV 

§ 1 (to Ch. XIV, § 5). When the interest rate varies, there are 
two rival concepts of " standard income " 396 

§ 2 (to Ch. XIV, § 12). Effect of foreknown tax on increase of 
capital 398 

§ 3 (to Ch. XIV, § 13). Unrestricted application of a true income 
tax impracticable •• • 400 



ANALYTICAL TABLE OF CONTENTS xxi 

Appendix to Chapter XVI 

PAOB 

§ 1 (to Ch. XVi, § 6). Mathematical coefficients of proTjability, 

caution, and risk 403 

§ 2 (to Ch. XVI, § 7). Formula for mathematical value of a risky- 
bond 403 

§ 3 (to Ch. XVI, § 10). Variability about a mean, as measured 
by the " standard deviation " 406 

§ 4 (to Ch. XVI, § 20). Method of computing a pure level life 
insurance premium 410 

INDEX 413 



INTRODUCTION. Fundamental Concepts 

Chapter I. Wealth 
Chapter II. Property 
Chapter III. Utility 



THE NATUEE OF CAPITAL AND INCOME 

CHAPTER I 

WEALTH 
§ 1 

The term " wealth" is used in this book to signify material 
objects owned by human beings. According to this defini- 
tion, an object, to be wealth, must conform to only two 
conditions : it must be material, and it must be owned. To 
these, some writers add a third condition, namely, that it 
must be useful. But while utility is undoubtedly an essen- 
tial attribute of wealth, it is not a distinctive one, being 
implied in the attribute of appropriation ; hence it is redun- 
dant in a definition. Other writers, like Cannan, while 
specifying that an object, to be wealth, must be useful, 
do not specify that it must be owned. They therefore 
define wealth as " useful material objects." This definition, 
however, includes too much. Rain, wind, clouds, the 
Gulf Stream, the heavenly bodies — especially the sun, 
from which we derive most of our light, heat, and energy 
— are all useful, but are not appropriated, and so are not 
wealth as commonly imderstood. Still other writers 
insist that an article, to be wealth, must be "exchangeable." 
But this restriction would exclude parks. Houses of Par- 
hament, the Hague Temple of Peace, and much other 
trusteed wealth ; all wealth, in fact, which happens to fall 
into permanent hands. Although it is essential that wealth 
should be owned, it is not essential that it should contin- 

3 



4 NATURE OF CAPITAL AND INCOME [Chap. I 

ually change owners. Again, many writers, like McLeod, 
omit the quaHfier "material" altogether, in order to 
make room for the inclusion of such "immaterial wealth" 
as stocks, bonds, and other property rights, and for human 
and other services. Property and services are, it is true, 
inseparable from wealth, and wealth from them, but they 
are not wealth. To embrace all these under one term 
involves a species of triple counting. A railway, a railway 
share, and a railway trip are not three separate items of 
wealth; they are respectively wealth, a title to that 
wealth, and a service of that wealth. Finally, a few econo- 
mists, like Tuttle, have endeavored to break away from 
concrete objects entirely. The term " wealth," they main- 
tain, applies, not to the concrete objects, but to the value 
of these objects. Much may be said in support of this 
contention. But as the question is chiefly verbal, that is, 
not a question of finding a suitable concept, but of finding 
a suitable word for a concept, it does not seem advisable 
to depart from the prevailing usage among economists. 

Wealth, then, includes all those parts of the material 
universe which have been appropriated to the uses of 
mankind. It does not include the sun, moon, or stars, 
because no man owns them. It is confined to this little 
planet, and only to parts of that ; namely, the appropriated 
portions of the earth's surface and the appropriated objects 
upon it. The appropriation need not be complete; 
it is often only partial and for a particular purpose, 
as in the case of the Newfoundland Banks, which are appro- 
priated only in the sense that the fishermen of certain 
nations have the right to take fish in their vicinity, while 
their waters are open to all men for all other purposes. 
In fact, it is doubtful if there are any objects owned so 
unrestrictedly that the owner of them may use them in 
absolute defiance of the wishes of others. By appropriation 
of any object is therefore meant that degree of appropria- 
tion to which the object is subjected. 



Sec. 2] WEALTH 5 

Any single object of wealth is called an article of wealth, 
an item of wealth, or an instrument. The term "instru- 
ment" is perhaps the most convenient. It appears to 
have been first employed by John Rae in 1834.^ 

§ 2 

Various classes of wealth may be distinguished. Wealth 
which consists of the earth's surface is called land; any 
fixed structures upon it, land improvements; and the two 
together, constituting immovable wealth, real estate. 
All wealth which is movable (except man himself) we 
shall call commodities. A third group includes human beings 
— not only slaves who are owned by other human 
beings, but also freemen who are their own masters. 

It is true that freemen are not ordinarily counted as 
wealth; and, indeed, they are a very peculiar form of 
wealth, for various reasons: first, because they are not, 
like ordinary wealth, bought and sold; secondly, because 
the owner usually estimates his own importance so much 
more highly than any one else ; and finally, because the 
owner and the thing owned in this case coincide. Yet 
they are, like other wealth, "material" and "owned." 
These attributes, and others which depend on them, justify* 
the inclusion of man as wealth. But in order to concede as 
much as possible to popular usage, the following supple- 
mentary definition is framed: By wealth (in its more 
restricted sense) we mean material objects owned by man and 
external to the owner. This definition obviously includes 
slaves, but not freemen. But it is more difficult of appU- 
cation than the wider definition first given, as it requires 

^ New Principles of Political Economy, recently reprinted under the 
title Sociological Theory of Capital, Macmillan, 1905. 

^ Among those writers who have included man in the category of 
wealth are Davenant, Petty, Canard, Say, McCuUoch, Roscher, Witt- 
stein, Walras, Engel, Weiss, Dargun, Ofner, Nicholson, and Pareto. 



6 NATURE OF CAPITAL AND INCOME [Chap. I 

US to separate into arbitrary classes those persons who are 
intermediate between freemen and slaves, such as vassals, 
indentured servants, long-time apprentices, and negroes held 
in peonage. A man bound out to service for thirty years 
is almost indistinguishable from a slave, and if the term of 
service be long enough and the control absolute enough, 
the distinction becomes a distinction without a difference. 
On the other hand, the shorter the term of service, the 
nearer does his condition approach freedom. As a matter 
of fact, most workers in modern society are "hired," i.e. 
bound by contract to some extent and for some period of 
time, even though it be for no more than an hour, and to 
that extent are not free. In short, there are many degrees 
of freedom and many degrees of slavery, with no fixed 
line of demarcation. 

Two concepts have been defined which may be des- 
ignated as "wealth in its more general sense " and " wealth 
in its more restricted sense." There need be no confusion 
between them. Ordinarily, when the simple term " wealth ' ' 
is used, the former concept will be understood, and any 
propositions which hold true of this broader concept will 
necessarily apply also to the narrower one. If we have oc- 
casion at any time to refer to the latter exclusively, we may 
always make use of the full phrase, "wealth in its more 
restricted sense." 

There are many admissible ways of classifying wealth, 
one being more or less desirable than another ac- 
cording to the purpose for which it is intended. The 
scheme on page 7 is not based on any one logical cri- 
terion, but is intended merely to give the principal groups 
into which wealth, as it actually exists, naturally falls. 
It scarcely needs to be stated that the various classes are 
not always absolutely distinct. Like all classes of concrete 
things, they merge imperceptibly from one into another. 
For this reason the classification is of httle importance 



Sec. 2] 



WEALTH 



except to give a bird's-eye view of economic science. 
In fact, the classification of concrete things is seldom of 
paramount importance in scientific study. Not classifica- 
tion, but analysis, solves scientific problems.^ 



^ 



riand ] 



productive land 



ways of transit - 



. building land 



f crop land 
grazing land 
timber land 
mining land 
hunting land 
fisheries 

' railways 
roadways 
waterways 

. parks 



land improvements - 



' buildings 
improvements on 
highways 
L minor 



f overhead 

underground 

surfacing 
. bridging 



o 



"3 



r mineral 
raw materials -! agricultural 

[ manufactured 



finished 
products 



slaves 
free 



r by being burned 
consumable -! by being eaten or drunk 
[ by being otherwise used 

mechanical devices 
animals 
"hard money" 
. durable -I clothing and jewelry 

furniture and works of art 
reading matter 
L minor 



^ See the writer's "What is Capital?" Economic Journal, Decem- 
ber, 1896, p. 516; and "Precedents for Defining Capital," Quarterly 
Journal of Economics, March, 1904. 



8 NATUEE OF CAPITAL AND INCOME [Chap. I 

§ 3 

In the definition of wealth were included two attributes : 
wealth is material; and, it is owned. These attributes, 
materiality and appropriation, need to be considered sepa- 
rately. The remainder of this chapter will be devoted to 
the former. 

An important and useful result of the materiality of 
wealth is that it provides a basis for the physical measure- 
ment of wealth. Wealth is of many kinds, and each kind 
is measured in its own proper physical unit. These units 
have been handed down to us from various sources and in 
great diversity, but all of them are in the last analysis 
arbitrary. 

Many kinds of wealth are measured by weight-units. 
This is true of coal, iron, beef, and in fact, of most 
"commodities." Each unit consists of the weight of 
some particular piece of matter which is adopted for con- 
venience as a standard. For instance, the English pound is 
simply a lump of platinum kept in London and called ar- 
bitrarily the pound. 

Many articles are not so conveniently measured by 
weight-units as by space-units, whether of volume, area, or 
length. Thus we have, for volume, milk measured by the 
quart, wheat by the bushel, wood by the cord, and gas by 
the cubic foot ; for areas, we have lumber sold by the square 
foot and land by the acre; for length, we have rope, wire, 
ribbons, and cloth measured in feet and yards. All these 
units of length, area, and volume are also quite arbitrary 
or conventional. The definition of the English yard, for 
instance, is an imaginary line drawn between two small 
dots on gold plugs in a particular brass rod in London. 

Many articles exist in more or less definite units which 
need only to be counted, as for instance, eggs or oranges, 
which are measured by the dozen. Similarly, writing paper 
is reckoned by the quire ; pencils and screws by the gross. 



Sec, 3] WEALTH 9 

In such cases we say that the article is measured 
by number. But "number" is by no means peculiar to the 
last-named case. All measurement implies both an ab- 
stract number, and a concrete unit, as "ten screws," "six 
eggs," or "four pounds-of-granulated-sugar." 

The last example suggests that in order to specify fully 
the unit of any kind of wealth, it is necessary to enumerate 
its particular attributes, or enough of them to distinguish 
it from other sorts of wealth with which it may become con- 
fused. Thus, it is often necessary to specify what "grade" 
or "brand" is meant, as "Grade A," "Eagle Brand," 
"Lackawanna" coal. Sometimes the special sort is denoted 
by a trade mark or hallmark. It is in this way that the 
attributes of particular kinds of wealth enter into the con- 
sideration of economic science, and not, as some have er- 
roneously supposed, separately as an "immaterial" sort of 
wealth. The "fertility" of land is not to be counted as 
wealth apart from the land itself; it is the "fertile land" 
which is wealth. The "skill" of a mechanic is not wealth 
in addition to the man himself; it is the "skilled me- 
chanic" who should be put in the category of wealth. 

Of course, the number expressing the measure of wealth 
may be unity, as for instance, "one dwelling." Sometimes 
there is only one article of the particular kind in existence. 
There is but one Battery Park, one Buckingham Palace, 
one Koh-i-noor diamond, one Rhynd papyrus. Dealers 
call such articles "uniques." Strictly speaking, every ar- 
ticle might be called a unique, even as no two grains of 
wheat are precisely alike; but for practical purposes we 
overlook minor differences and regard articles sufficiently 
similar as homogeneous. 

§ 4 

Thus each individual kind of wealth may be measured in 
its own special unit, — pounds, gallons, yards ; but for most 
purposes it is more important to measure the value of wealth. 



10 NATURE OF CAPITAL AND INCOME [Chap. I 

and this may be done in dollars and cents, pounds and shil- 
lings, francs and centimes, and so forth. This is also a spe- 
cies of physical measurement, but involves the principle of 
exchange. So much mystery has surrounded the term 
''value" that we cannot be too careful to obtain correct 
and simple ideas on the subject. In the explanation which 
follows, the concept of value is made to depend on that 
of price; that of price in turn on exchange; and finally, 
that of exchange on transfer. 

An article of wealth is said to be transferred when it 
changes owners. It is to be observed that such a change 
does not necessarily imply any change of place. Ordinarily, 
the transfer of an article involves change in its posi- 
tion. The purchase of tea or sugar is accompanied by 
the delivery of these articles across the counter from dealer 
to customer. But in many cases such a change of position 
does not occur, and in the case of real estate it is even im- 
possible. This distinction between change of ownership 
and change of position is not always borne in mind. It is 
sometimes said, for instance, that exports and imports 
must balance in a certain manner. But if by "exports" 
we mean articles that are sent out of the country, and by 
''imports" those which come into it, the proposition will 
not hold true. When, some years ago. Englishmen were 
buying American breweries, these articles, of course, 
were not exported, though they were transferred to foreign 
ownership. 

Transfers may be voluntary or involuntary. Examples 
of involuntary transfers of wealth are transfers effected 
either (1) through force and fraud of individuals, as in rob- 
bery, burglary, embezzlement, etc.; or (2) through force 
of government, as in taxes, court fines, etc. But at present 
we have to do with voluntary transfers. 

Voluntary transfers are of two kinds : (1) one-sided trans- 
fers, i.e. gifts and bequests ; and (2) reciprocal transfers or ex- 
changes, which are the most important for economic science. 



Sec. 5] WEALTH 11 

Exchange of wealth, then, means the mutual and volun- 
tary transfer of wealth between two owners, each transfer being 
in consideration of the other. If either of the two quanti- 
ties of wealth exchanged is divided by the other, the 
quotient is called the price of the latter. Thus, when three 
bushels of wheat are traded for two dollars of gold, the 
price of the wheat is § of a dollar per bushel, and the price 
of the gold is IJ bushels of wheat per dollar. In modern 
times, one of the two articles is usually money, but this 
condition is not essential, and in primitive times was not 
even common. When the exchange is one of money for 
other wealth, it is called a purchase (with reference to the 
one who parts with the money) and a sale (with reference 
to the person who receives the money). 



§ 5 

In order that there may be a price, it is not necessary 
that the exchange in question should actually take place. 
It may be only a contemplated exchange. A real estate 
agent often has an "asking price," that is, a price at which 
he tries to sell, usually above the price of an actual sale. 
In the same way there is often a "bidding price," which is 
usually below the price of actual sale. The price of sale 
thus generally Ues between the prices first bid and asked. 
But it sometimes happens that the bidder refuses to raise 
his bid and the seller refuses to lower his asking price. 
In such a case no sale takes place and the only prices are 
those bid and asked. Trade journals report, for many 
commodities, the price of sale if there is a sale, otherwise 
the two prices bid and asked, or if both do not exist, the one 
which does. 

When there is no sale, and especially when there is no 
price bid or asked, it is not so easy to answer the question. 
What is the price? Recourse is then had to an "appraise- 
ment" or appraisal, which is simply a more or less skilful 



12 NATUKE OF CAPITAL AND INCOME [Chap. I 

guess as to what price the article would or should fetch. 
Appraising or guessing at prices is often very difficult in 
practice. It is necessarily employed, however, by the gov- 
ernment in assessing taxes and customs and condemning 
land ; by insurance companies in settUng claims and adjust- 
ing losses ; by merchants in making up inventories and other 
statements; and by statisticians and others. In fact, 
some people make a living by simply appraising wealth on 
which, for one purpose or another, a price of some sort must 
be set. Evidently, the purpose makes a great difference in 
the appraisal. Sometimes we need to know the price for 
which an article could be sold at an immediate forced sale; 
sometimes, what it might be expected to bring if a reason- 
able time were allowed ; sometimes, what the owner would 
probably take; sometimes, what a possible purchaser 
would probably give. These appraised prices may all be 
different. A family portrait may be worth an untold 
amount to the owner, but might bring next to nothing if 
actually sold. The owner would endeavor to appraise it at 
a high figure if he wished to insure it against fire; but if 
he wished to borrow money on it, the appraisement would 
doubtless be small, for the pawnbroker would consider it 
almost worthless. 

Thus, in practically making an appraisement we encoun- 
ter many difficulties, owing partly to the unknown char- 
acter and condition of the parties involved, and partly 
to the variety of interests to be served by the appraisal. 
But whatever the difficulties and ambiguities in as- 
certaining a price or prices for any article, the price or 
prices do actually exist without ambiguity. The vague- 
ness comes wholly from failure to specify sufficiently the 
conditions under which the exchange is to take place. If 
we specify in sufficient detail the conditions of the contem- 
plated exchange, its terms will be quite definite ; but whether 
or not we can guess at those terms correctly is quite another 
matter. 



Sec. 6] WEALTH 13 

§ 6 

Having obtained the price of any kind of wealth, we may 
compute the value of any given quantity of that wealth, 
without necessarily supposing that particular quantity to 
be exchanged. The value of a given quantity of wealth is 
found by multiplying the quantity by the price. Thus, if 
the price of wheat is § of a dollar per bushel, then a lot 
consisting of 3000 bushels would have a value of 3000 x 
$1 per bushel or $2000. In other words, the value of a 
certain amount of one kind of wealth is the quantity of 
some other kind for which it would be exchanged, if the 
whole amount were exchanged at the price set upon it. 
The exchange which sets the price need not be the ex- 
change of the particular 3000 bushels which we are valuing ; 
some other exchange of, say, 300 bushels for $200 may set 
the price. This is one reason why it is preferable to ex- 
plain price first and value afterward. 

The definition of value which has been given, applying, 
as it does, to an aggregate of wealth instead of the unit, 
departs somewhat from economic usage; but it follows 
closely the usage of business men and practical statisti- 
cians. Economists have not usually thought it necessary 
to distinguish between the purchasing power of the unit 
and the aggregate, but have employed the term "value" 
indiscriminately to both. In other respects also their usage 
has been somewhat different from that here employed. 
Some of them have confined "price" to a money expression, 
i.e. to what is here called money price, and appHed the term 
"value" to purchasing power in "goods." Others have 
used the term "price" in the sense of what an article ac- 
tually sells for (market price) and "value" in the sense of 
what it ought to sell for (appraised price or reasonable price). 
Others, in turn, have used the term "price "in the sense em- 
ployed in this book, but "value" in the sense of the degree 
of esteem in which an article is held ("marginal utility" 



14 



NATURE OF CAPITAL AND INCOME 



[Chap. I 



or "subjective value"). It seems preferable to conform 
our definitions of value and price as closely as possible to 
business usage, which instinctively and consistently apphes 
the term " price" to the unit and " value " to the aggregate. 

§7 

The distinction between quantity, price, and value of 
wealth may be seen clearly in any "inventory," such as the 
following : — 





Quantity 


Pbice in 
Wheat 


Value in 
Wheat 


Shoes 

Beef 

Dwelling House . . . 
Wheat 


1000 pair 
300 lbs. 
1 house 
100 bu. 


4J bu. per pair 
i bu. per lb. 
10,000 bu. per house 
1 bu. per bu. 


4,250 bu. 

60 bu. 

10,000 bu. 

100 bu. 








14,410 bu. 



In the first column are recorded various quantities 
of wealth, measured each in its own special unit ; in the sec- 
ond column are the prices of these in wheat ; while in the 
last column are their values, also in terms of wheat. The 
first and last columns represent two different modes of meas- 
uring wealth. Statistics of wealth, such as those pubhshed 
monthly by the Department of Commerce, usually give 
both "quantities" and "values." To translate from one 
to the other we need always a price as go-between. 

It is important not to confuse the three columns with 
each other. The quantity of beef is a totally different thing 
from its value, and each of these is different from its price. 
The quantity is measured in pounds of beef, its value in 
bushels of wheat, and its price in bushels per pound. These 
three magnitudes are all of different "dimensions." Both 
quantity and value are simply physical magnitudes. 
"Value" as here explained is not a subjective magnitude 



Sec. 7] WEALTH 15 

in the mind of man, but purely objective, as money value, 
or wheat value. It has, of course, subjective causes, but 
these do not concern us yet.^ 

The measurement of wealth in "value" has this great 
advantage over its measurement in "quantity," that it 
translates the many kinds of wealth into a single kind. 
All the items in the third column of the inventory are thus 
expressed in a common unit, the bushel. We may conse- 
quently add together this column and obtain a single sum, 
namely, 14,410 bushels ; but summation of the first column 
is impossible, because shoes, pounds of beef, houses, and 
bushels of wheat are incommensurable. We see here one 
of the important functions of money ; it brings uniformity 
of measurement out of diversity. 

But, although this reduction to a common measure is 
practically convenient, it would, of course, be a great mis- 
take to suppose that it gives what may be called "the true 
measure of wealth." "The value of wealth" is an incom- 
plete phrase; to be definite we should say, "the value of 
wealth in terms of gold," or in terms of some other particu- 
lar article. We cannot, therefore, use such values for 
comparing different groups of wealth except under certain 
conditions and to a Hmited degree. To compare the 
wealth-values of America and England, of Ancient Rome and 
Modern Italy, of Carnegie and Crcesus, will give different 
results according to the standard of value employed. 

§8 

We have seen how to measure the three magnitudes, — 
quantity, price, and value of wealth. This measurement 
is, practically, a very inaccurate affair. The degree of ac- 
curacy attained is exaggerated in the minds of most per- 
sons, even including business men. In measurements of 
quantities of wealth there are two sources of error, for every 

* Further explanation as to the dimensions of the quantity, price, 
and value of wealth are given in the Appendix to Chap. I, § 1. 



16 NATURE OF CAPITAL AND INCOME [Chap. I 

measurement includes, as we have seen, two elements: 
a unit of measure, which may be inaccurate ; and a number 
or ratio between the quantity to be measured and the unit, 
which number may also be inaccurate. In modern times 
the first source of error is practically ehminated. Our 
units of weight and measure are standardized by law, and 
a pound weight in CaUfornia is equal to one in Connecticut, 
within one part in many thousand. The chief source of 
error, therefore, Hes not in the unit, but in the ratio of the 
wealth to that unit. In retail trade the inaccuracy is as 
great as five per cent, or greater. Wholesale transactions 
are more accurate. A large manufacturing concern of 
Syracuse had its measurement of the weight of caustic 
soda sold in carload lots compared with the measurement 
made by its customers, and the results agreed within one 
fifth of one per cent on two fifty-carload lots. Probably 
the greatest degree of accuracy ever obtained in com- 
mercial measurements is on the Mint scales used by the 
United States in Philadelphia and San Francisco. These 
scales weigh accurately to within about one part in ten 
million. 

When we proceed from quantities of wealth to values, 
we introduce still a third source of inaccuracy, namely, in 
the price factor by which we multiply. This is especially 
true if the price be merely an " appraised " price. The price 
of any actual sale is an absolute fact and cannot be said to 
have any inaccuracy; but the price at which we estimate 
that a thing would sell under certain conditions is always 
uncertain. In the case of staple articles, i.e. articles regu- 
larly on the market, a dealer can often appraise correctly 
within one per cent. Real estate in certain parts of a city 
where sales are active can sometimes be appraised correctly 
within five or ten per cent; but in the "dead" or out-of- 
the-way parts of some towns, where sales are infrequent, the 
appraisement becomes merely a rough guess. Again, in 
the country districts, while farms in the settled parts of 



Sec. 8] WEALTH 17 

Iowa and Texas can be appraised within ten or fifteen per 
cent, in the backward parts even an expert's valuation is 
often proved wrong by more than fifty per cent. In some 
cases, in fact, where a sale of the article is scarcely conceiv- 
able, an appraisement is almost out of the question. To 
estimate the value of the Yellowstone Park is impossible, 
unless we allow ourselves a range of several hundred per 
cent. Similar wide limits must be allowed when we try 
to value free human beings. We can often give a lower 
limit, but seldom an upper one. The estimates may vary 
enormously with the point of view. It is sometimes said, 
"If I could buy Mr. So-and-So at my valuation and sell 
him at his, I'd get rich." It would be wrong, however, to 
conclude, as some writers have, that because we cannot 
value them accurately, public parks or freemen cannot be 
called wealth. When the slaves in the South became free- 
men they ceased to be appraised as wealth. The result 
has been somewhat confusing to our census statistics. 
The Manufacturers' Record of Baltimore recently issued 
figures showing a sharp drop in the assessed valuations of 
wealth in the South after the war, and the inference was 
drawn that wealth had immensely decreased. But a large 
part of this so-called decrease consisted merely in the change 
of ownership of slaves from their old masters to themselves, 
and the consequent omission of them from the statistics. 

Various writers, from Petty down to Engel and Nichol- 
son, have tried to assess the value of human beings. 
Professor Nicholson estimates roughly that the English 
nation is worth at least five times the value of other ex- 
isting wealth in England.^ Such calculations are of course 
of more theoretical than practical moment. They are also 
necessarily inaccurate, and involve in each case some par- 
ticular supposition as to the purpose of the appraisement ; 
for instance, whether it is to indicate the earning power of 
the population, their value to themselves, or to others. 

* Economic Journal, March, 1891, p. 95. 
c 



CHAPTER II 

PROPERTY 



The definition of Wealth in the previous chapter restricts 
its meaning to concrete material objects. But economics 
has also to deal with abstract services, utilities, and property- 
rights. These, like material wealth, are bought and sold, 
and are, in fact, often regarded as a sort of "immaterial" 
or " incorporeal " wealth. It is, however, needless as well as 
confusing to include these elements under the general cate- 
gory of wealth. They are not wealth, though they are 
intimately related to wealth. The definition given shows 
that wealth has two attributes: it must be material, and 
it must be owned. Its materiality was the subject of the 
previous chapter; its ownership will be the subject of the 
present chapter. 

But what is meant by owning wealth? We answer: 
to have the right to use it. Such a right is called 'prop- 
erty, or, more explicitly, a property right. To own a loaf of 
bread, or to have property or proprietorship in it, means 
nothing more nor less than to have the right to eat it, or sell 
it, or otherwise employ it to satisfy one's desires. To own 
a suit of clothes is to have the exclusive right to wear it. 
To own a carriage is to have the right to drive in it or 
otherwise utilize it as long as it lasts. To own a plot 
of land means to have the right to its use forever. The con- 
cept of property — the "right to use wealth" — is more 
fully expressed by the phrase, the "right to the uses of 
wealth." In this phrase we have to deal with two new 
ideas — rights and uses — each of which needs to be treated 

separately. 

18 



Sec. 2] PROPERTY 19 

§2 

We need first to understand what is the nature of the uses 
or services of wealth. The services of an instrument of 
wealth are the desirable changes effected (or the undesir- 
able changes prevented) by means of that instrument. For 
instance, the services of a loom consist in changing yarn into 
cloth, or what is called weaving. Similarly, a plow per- 
forms the service of changing the soil in a particular manner ; 
a bricklayer, of changing the position of bricks. A dam 
or dike performs the service of preventing the water from 
overflowing the land; a fence, of preventing cattle from 
roaming; a necklace, of sparkling or reflecting light, and 
thereby satisfying the love of beauty or the vanity of the 
owner. 

When services are described as desirable events, it is 
meant that they are desired or esteemed by the owner or 
owners, not necessarily by every one, or even any one, else. 
It may even happen that the events are distinctly distaste- 
ful to others. A factory whistle may be a nuisance to every 
one except the factory owner. 

In this connection it is important to distinguish between 
the uses or desirable events, and the utility or desirability 
of those events. The desirable service is a thing; it is 
usually objective. The desirability of the service, on the 
other hand, is a quality, and is purely subjective. It is 
a feeling toward the events, not the events themselves. 
In the present chapter we do not have to deal with the de- 
sirability, and it will form the subject of the next chapter. 

Each sort of service is measured in its own appropriate 
unit. Sometimes the measurement is by number, i.e. 
obtained by simply counting the acts in which the specified 
service consists, as, for instance, in the case of the strokes 
of a printing press ; sometimes the measurement is by time, 
as in the case of the day laborer; while sometimes the 
measurement of the services is expressed in terms of the 



20 NATURE OF CAPITAL AND INCOME [Chap, II 

units of wealth affected by those services, as in the case of 
so-called piecework. The services of a miner are meas- 
ured by reference to the quantity of coal mined ; the serv- 
ices of a planter, by the number of acres planted ; and of a 
spinning machine, by the number of yards spun. Services, 
like wealth, are subject to exchange and, in consequence, 
have prices. The quantity of any service multiplied by its 
price gives its value. When reduced to value in a common 
standard, all varieties of services become commensurable 
with each other and with wealth. 

The opposite of a service is a disservice, which is an un- 
desirable change effected (or a desirable change prevented) 
by means of wealth. For instance, a locomotive renders 
disservices by consuming coal; a farm, by requiring fer- 
tilizers and labor ; a factory, by requiring costs of work- 
ing. Disservices, like services, are measured in quantity 
by special units and made commensurable in value by 
reduction to a common standard. 

§ 3 

Having seen what is meant by services of wealth, we next 
ask what is meant by the right to those services. "Right" 
is a term of jurisprudence, and brings economics into con- 
tact with the whole subject of legal and custom-sanctioned 
relations; but, for our present purpose, it is not necessary 
to go far in this direction. The right of a person to the 
uses of an article of wealth may be defined as his liberty, 
under the sanction of law and society, to enjoy the services 
of that article. 

Lawyers distinguish between property rights and per- 
sonal rights; but, to the economist, all rights are proprie- 
tary. The distinction between property and personal 
rights exists only so long as we restrict the meaning of 
wealth to the narrower of its two definitions, that is, only so 
long as we exclude free human beings. Here we have an 
instance in which logical convenience is served by adopting 



Sec. 3] PEOPERTY 21 

the broader definition of wealth, which includes human 
beings even when free, and by adopting also a coextensively 
broad definition of property so as to include all rights known 
to jurisprudence. This being premised, it follows that 
every right is a property right. No rights have ever been 
suggested which are not rights to obtain and enjoy the 
uses of wealth, either persons or things. Even the "right 
to fife, liberty, and the pursuit of happiness" is simply 
one's right to certain uses of his own person. The rights 
of a husband over his wife and of a wife over her husband, 
and the reciprocal rights between parents and children, as 
well as all other rights in 'personam, are claims against par- 
ticular persons; while the right to reputation, to the free 
exercise of one's calling, to immunity from boycott, perse- 
cution, etc., are claims upon the community generally.^ 
These rights are not ordinarily called property rights, just 
as persons are not ordinarily called wealth, and for a similar 
reason, — they do not enter into trade. When wives 
were bought and sold they were regarded as wealth, and 
marital rights as property. To-day, both are taken out of 
commerce and therefore removed from commercial ideas 
and terms. The economist need not, perhaps, absolutely 
insist on restoring them ; like the business man, he is chiefly 
interested in what is salable. But in framing his defini- 
tions he finds it difficult, if not impossible, to confine the 
terms "wealth" and "property" to objects which are ex- 
changeable, without thereby sacrificing simplicity and logi- 
cal convenience, and excluding certain objects, such as public 
parks and former Enghsh entails, which, though never sold, 
even business men would call wealth and property respec- 
tively. We therefore choose in this book to frame our defi- 
nitions so as to include such elements, even though they be 
not further referred to. In definitions, it is usually better 
to include too much rather than too little, and in this case, 

1 Cf. T. E. Holland, Jurisprudence, Macmillan, 1898, pp. 50, 80, 87, 
90, 128. 



22 NATURE OF CAPITAL AND INCOME [Chap. II 

at least, the superfluous which is included will seldom con- 
cern and never embarrass us. 

Property rights, then, consist of rights to the uses or 
services of wealth. But the services which we own are al- 
ways and necessarily future services; the past have per- 
ished. Moreover, since all future events are uncertain, we 
are always constrained to reckon with the element of chance. 
A strictly complete definition of a property right, therefore, 
would read as follows : A property right is the right to the 
chance of obtaining some or all of the future services of one 
or more articles of wealth. 

Property is measurable, just as are wealth and services, 
each in its own particular unit. Usually the measurement 
is "by number," that is, by counting the number of rights 
of the same kind. Thus, one hundred shares of preferred 
stock in a particular company is a statement of the amount 
of that particular property. The concepts transfer, ex- 
change, price, and value apply to property as to wealth and 
to services. Indeed, as an exchange of wealth is but a con- 
cealed exchange of services, so an exchange of services is but 
a concealed exchange of the right thereto, namely, prop- 
erty. Hence the exchange of property is the final form 
of exchange, and includes in itself all other forms whatso- 
ever, 

§4 

Wealth and property, then, are correlative terms. 
Wealth is the concrete thing owned; property is the ab- 
stract right of ownership. The two concepts mutually 
imply each other. There can be no wealth without prop- 
erty rights applying to it, nor property rights without wealth 
to which they apply. In fact, the proposition that 
property and wealth are coextensive follows neces- 
sarily from the definitions of wealth and property 
which we have adopted. But it may readily be objected 
that in the actual concrete world, for which these defini- 
tions were designed, the correspondence between what are 



Sec. 4] PROPERTY 23 

known as wealth and property does not hold true. A thor- 
ough examination of the case, however, will remove this 
objection. 

Sometimes wealth and property rights are so closely 
associated as to be confused with each other, so that, un- 
less one stops to consider the matter, the existence of the 
two separate concepts would not be suspected. This is 
true in the case of "fee simple," where a piece of 
land is spoken of as a "piece of property." For prac- 
tical purposes, little objection can be raised to such popular 
usage, but even in such cases strict accuracy requires that 
the two ideas should be distinguished. The distinction is 
more easily remembered if we employ the full phrase "prop- 
erty right." A loaf of bread is concrete wealth, not a prop- 
erty right; the right to eat it is the property. On the 
other hand, in the more involved cases of property rights, 
we encounter the opposite difficulty. The danger here is in 
separating the concepts of wealth and property too far, 
so as to consider them as independent instead of interde- 
pendent. When railway shares are sold in Wall Street, the 
investor is prone to think of those shares as entirely de- 
tached from any concrete wealth. It is unlikely that he 
has ever seen or ever will see the steel rails, cars, and loco- 
motives upon which those shares are based; and indeed, 
the only concrete object of which he is Hkely to be dis- 
tinctly conscious is the paper certificate itself. But it 
is clear that this paper certificate is not itself the prop- 
erty, but merely the written evidence of it and that the 
railway shares, to be property, involve a real railway 
(v>^ealth) underneath. 

That all wealth involves a property right is not likely 
to be denied by any one; and that all property rights in- 
volve underlying wealth should be equally evident. But 
this is not the case. In fact, some of the most dangerous 
fallacies which beset the business world, including many of 
the sophisms of credit, are due to the difficulty of recog- 



24 NATUEE OF CAPITAL AND INCOME [Chap. II 

nizing the wealth lying behind property in some of its sub- 
limated forms. 

§5 

In order not to devote too much space to this subject 
the best procedure will be to give types of the chief forms 
of property, and to specify in each case what wealth under- 
lies the right. This is done in the table on pages 26 and 
27, which also specifies the services involved, and (where they 
exist) the certificate or written evidence of the property 
right. 

§6 

Probably ninety per cent of the actual property in the 
United States would be included under the cases entitled 
Fee Simple, Partnership Rights, Stocks, Bonds, Notes, and 
Lease Rights. In all of these cases, the existence of the 
real wealth behind them is well known and acknowledged. 
For practical purposes, therefore, the proposition that 
wealth and property are coextensive is already established. 

Of the remaining cases some seem a Uttle obscure at 
first, but they may be readily solved if we bear in mind a 
few general principles : 

The first thought which should guide us is that, given 
any particular property right, we should first discover the 
benefits or "services" secured by that right, then the phys- 
ical means by which those services are obtained. These 
means are not always identical with the "cause" of those 
services. For instance, real estate with a southern ex- 
posure is especially desired because of the sunlight which 
falls upon it. The sun may be called the cause of the sun- 
light, but the land is the practical means of obtaining it. 
To own or not to own the land is to obtain or not to 
obtain the sunlight which goes with it. It is the land which 
puts the sunlight at the disposal of its owner. On the other 
hand, when a lamp gives its fight it is not only means, but 
also cause. 



Sec. 6] PROPERTY 25 

Following this idea, that wealth is simply the means 
and not necessarily the cause, we can better understand some 
of the items in the table. We see clearly what it is that lies 
behind a street railway franchise, or the franchise of the 
underground system of New York City. It must be the 
wealth by means of which the transportation can take place. 
The streets which the railway has the right to use form the 
necessary means for its transportation services. To own 
the streets involves the possession of the right to use them 
for transportation purposes, and, when this right is given 
or sold, as when a franchise is granted, this act constitutes 
a partial surrender of the ownership of the streets. 

Again, let us consider the case of a promise. The physical 
means of fulfilling a promise are. evidently the person who 
made the promise and the wealth which that person can or 
will use for that purpose. Thus, a debt or bond secured 
by a mortgage is primarily a claim upon the promisor which 
he may satisfy out of his earnings or his general wealth. 
But it offers this great advantage over other forms of 
indebtedness, that it is also a contingent claim upon a 
specific portion of the promisor's wealth, which may be 
taken in payment even against his will, if the promisor 
otherwise fails to make good his promise. Here the means 
of perfecting the right evidenced by the bond include the 
person of the promisor, his general wealth, and the specific 
part of that wealth covered by the mortgage. On the other 
hand, a "labor due" is principally a claim upon the person 
of the laborer, for he must be the means of performing the 
labor required. In country districts farmers are often 
under obUgations to the county to furnish a certain amount 
of roadwork of men and horses. The right to such work 
is a species of property belonging to the county. A still 
better example is found in cases where the labor or services 
to be rendered are of a personal or artistic character, such 
as the singing of a Patti or the acting of a Bernhardt ; for, 
while one under contract to lay bricks might reasonably 



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28 NATURE OF CAPITAL AND INCOME [Chap. II 

fulfil his contract by furnishing another equally skilful 
bricklayer, no audience attracted by either of those artists 
would accept in return for its entrance money the perform- 
ance of any understudy, no matter how capable. This 
right to the services of a particular person, as distinguished 
from the right to services of a particular character, gives 
rise to many curious cases in law. Similarly, a personal 
note is to a large extent a claim upon the person of the 
drawer, though also a claim upon his other wealth; for 
both the man himself and his external wealth are the means 
of keeping good the promise and finally paying the debt. 
Another case is that of a ''factor's agreement" or some 
other promise by which a firm or person agrees to refrain 
from certain acts, such as selling in competition with the 
promisee. Some years ago a paper manufacturer near New 
Haven was offered a round sum if he would close his mills. 
This he did, to the benefit of both himself and his former 
rivals, though not of the public. In this case the contract 
which he made with his rivals constituted a kind of prop- 
erty for them ; the wealth by means of which his promise 
was made good was evidently his own person, together with 
his plant ; and the service performed was the inactivity of 
both. 

Good will is a less certain though still a valuable form 
of property. A few years ago one of the largest newspapers 
in the United States was sold. The property included, 
besides presses, type, Hnotype machines, office building, etc., 
the items of overdue subscriptions and good will. An over- 
due subscription is a debt which constitutes a virtual prom- 
ise of the subscriber, and thousands of these in the aggre- 
gate make up a considerable value. By good will is meant 
something very similar; namely, the quasi-promise of the 
subscribers to continue to pay as long as the newspaper is 
sent to them and they are satisfied. These quasi-promises 
are also property, being almost equivalent to a signed agree- 
ment of the subscribers to the effect : "We hereby promise 



Sec. 6] PROPERTY 29 

to pay the annual sum of $8 to the PubHshing Com- 
pany, provided that and so long as its newspaper is received 
and is satisfactory." Thus good will is merely the right 
to a tacit, loose, and contingent promise of support and pat- 
ronage, less cost. The firm possessing good will owns a 
precarious yet valuable claim upon its patrons, namely, 
the chance of their continued patronage. The persons of 
these subscribers, and their other wealth, are what under- 
Ue the property right, because they are the means to the 
desired services to which those rights apply. Of course 
the chance of obtaining these services is very much less 
than it would be if the services were specifically promised ; 
but chance, either large or small, is involved in all property 
rights. 

In the same way, the ''custom" of a tailor or the "prac- 
tice" of a physician is simply the right to the chance of 
future patronage. 

A franchise in the sense of a monopoly privilege granted 
by a government is quite different from a street railway 
franchise. The object of the monopoly is to prevent cer- 
tain acts of certain persons. The means to that end are, 
in the last analysis, the persons who are constrained to 
refrain, and the wealth withdrawn from competition. 

We may similarly regard a copyright. RecalUng the 
case of the paper trust, part of whose property was the prom- 
ise of a paper manufacturer not to compete, we may regard 
a copyright as the right to a similar refraining from or re- 
straining of competition. At one time, an English pub- 
lisher would obtain the promise of an American publisher 
not to "pirate" his works. It would have been property 
of great value to the publishers of the Encyclopaedia Bri- 
tannica if they could have prevented the pirating of their 
work in this country. Prevention can now be accomphshed 
through the instrumentality of international copyright. 
The wealth underlying this property right is the wealth 
which, if employed in the specified line, would enter into 



30 NATURE OF CAPITAL AND INCOME [Chap. II 

competition with the property owner. It mainly consists 
of the persons and plants of possible competing publishers ; 
and it does not matter whether their inactivity — their non- 
competition — is purchased by a money payment or en- 
forced by government intervention. 

In like manner we may resolve the problem of irre- 
deemable paper money. Where this exists in its purest 
form, with no promise or intention of ultimate redemption 
by the government which issues it, it amounts to a forced 
loan, or rather, a levy. It is like a check drawn by the gov- 
ernment upon the public, which each individual is obliged 
to cash. It is an order to surrender on demand a certain 
amount of the community's goods. The government usu- 
ally employs paper money to obtain ammunition or sol- 
diers' supphes. The merchants who give these goods are 
forced to accept paper money in return, and allowed to 
recoup themselves by passing on these orders to others. 
In this way people are deluded into believing that no one 
really loses, but that the loss is perpetually passed on. The 
loss is shifted, but nevertheless it exists ; for, since a definite 
quantity of supplies has been abstracted from the pubUc 
by the government, it is clear that this much loss has been 
suffered, however it may be distributed by rotation. Thus, 
irredeemable paper money is a claim on the general wealth 
of a community. Of course it seldom occurs that it con- 
tinues irredeemable, and when it becomes redeemable it 
changes its character; for when the government assumes 
the obligation involved, it becomes a special claim upon 
the government gold and other wealth. 

A somewhat similar vague property right is the govern- 
ment's taxing power, which is the right to take from the 
individual so much of the services or product of his wealth 
as may be necessary for the pubhc good. The heavier 
the tax, the greater the reduction in the value of the in- 
dividual wealth of the community. It is well known 
that to nationaHze land, as Henry George proposed, means 



Sec. 7] PROPERTY 31 

merely to increase the tax upon it until all its value has 
been taxed out of it; that is, to take from the individual 
all of the services or profit of his landed wealth for the bene- 
fit of the pubhc, leaving him merely the empty shell of 
nominal ownership. The case is analogous to that of a per- 
son or a community which has mortgaged its wealth so 
heavily that the value of its services is entirely consumed 
in the payment of interest, and nothing is left with which 
to redeem the pledge. The same principle applies to all 
taxes, even when not carried to such an extreme. 

§7 

A second helpful guide in resolving the various obscure 
forms of property is found in the fact that one property right 
is often overlaid by another. For instance, a mill is owned in 
shares; a railway company owns some of those shares; a 
bank owns some of the railway shares; and John Smith 
owns some of the bank shares. It is evident that John 
Smith has a claim upon the wealth constituted by the mill, 
although his property is only distantly connected with it, 
and through several intermediate layers of property rights. 

A common example of such secondary relation between 
wealth and property occurs when the property is held in 
trust. At common law, the trustee is the legal owner ; but 
the law of equity recognizes the fact that the beneficiary is 
the true owner. He has a claim against the trustee, and the 
trustee holds the right to the wealth as against the rest of 
the world. The beneficiary must work out his rights 
through the rights of the trustee. 

Another good example is that of a claim upon a govern- 
ment, as, for instance, a government bond. This is really 
a claim against the community, for the government is 
merely an intermediary between the bondholder and the 
pubhc wealth which is taxed to satisfy the bondholder's 
claims. The government owns property only as a sort of 
trustee for the pubhc. The Boston Common is held by the 



32 NATURE OF CAPITAL AND INCOME [Chap. II 

city of Boston, but is really owned by the citizens, who are 
the true beneficiaries. Each individual who has the right 
to enjoy it is to that extent a part owner. 

It is not uncommon thus to have, between a property 
right and the wealth underlying it, several layers of prop- 
erty. A man who owns an ordinary foreign bank note has 
a claim upon the property of the bank. But the bank's 
property consists, for the most part, not of tangible wealth, 
but of promissory notes and other claims on merchants. 
These notes represent a part right in the wealth (including 
persons) of the community; consequently the holder of a 
bank note quite unconsciously owns a claim upon the dry 
goods, groceries, and other wealth of merchants, which make 
good the debts of these merchants to the bank. 

In the case of United States bank notes he also owns an 
alternative claim on government bonds, and therefore on 
the taxable wealth which makes these bonds good. It is 
erroneous to think of a bank note as representing simply 
money. This is true of gold certificates; for there are in 
the United States Treasury as many actual gold dollars as 
there are certificates in circulation. A bank note, on the 
other hand, is made good, not solely by the metallic reserve 
of the bank, but also by the other property or "assets," 
which the bank is constantly changing or transforming into 
cash. The Bank of England, for instance, had £60,000,000 
of notes out at a given date, and only £43,000,000 of gold 
in its vaults. But the £17,000,000 deficiency which thus 
seemed to exist was represented by securities, that is, other 
property held by the bank. 

§8 

A third guide is that the correspondence between prop- 
erty and wealth is a contemporaneous correspondence. 
That is to say, the existing property rights are rights to 
the use of existing wealth, so that existing wealth underlies 
all existing property rights. It would seem at first sight 



Sec. 8] PROPERTY 33 

that "credit" forms an exception, for credit is a present 
right to a future payment. But it is impossible to have a 
right to any future wealth which is not also a right to some 
present wealth as a means of securing that future wealth. 
The right to next year's fruit is a right to or in present fruit 
trees. The right to next year's wheat is a right to or in the 
present farm, farmer, and farm implements. The right to 
receive a future chair or table yet unmade is the right to or 
in the present person, tools, and other wealth of the car- 
penter, which are the means by which that chair or table 
is to be secured. To own a note falling due next year is 
a part right in the person and other "assets" of the prom- 
isor, and ceases to have value as soon as he ceases to be 
"good for it." The courts do not restrict a debtor in the 
disposition of his possessions prior to the maturity of a note. 
He may elect to squander these, and even to commit sui- 
cide. But such destruction of the present means of pro- 
viding for future payment carries with it the impairment 
or destruction of the value of the note. No future com- 
modities or benefits whatever can be owned in the present 
except as claims on certain requisites of their production 
now in existence. We cannot own next year's goods sus- 
pended in mid air, as it were, any more than we can fly a 
kite without a cord. There must always be some present 
means of controlling the future. Thus, credit, like every 
other property right, is a part right upon existing wealth. 
And not only is every right to a future benefit a claim 
on present wealth, but conversely, every claim on present 
wealth is a right to a future benefit. Owning rights to 
"futures" is therefore not an exceptional case, but the gen- 
eral one. As we have seen, all wealth is merely existing 
means toward future services, and all property, merely pres- 
ent rights to some of those future services. It is only 
through the future services that wealth and property are 
bound together at all. The sequence of ideas is, first, pres- 
ent wealth ; second, future services ; third, present rights to 



34 NATURE OF CAPITAL AND INCOME [Chap. II 

these future services and therefore to the present wealth 
which yields them. Property is thus always a right to the 
chance of a future benefit. It always contemplates 
both present and future time. We are here emphasiz- 
ing the fact that property always constitutes an inter- 
est in the present means for acquiring it. Property in 
nothing is nothing. This principle applies even to the 
extreme case of good will. We saw that good will is the 
ownership of a chance of continued patronage. The future 
patronage may in some cases include that of persons yet 
unborn; but the road to their patronage must lie through 
the present generation. Existing persons and things must 
always constitute the means for the attainment of any 
benefits expected in the future. 

§9 

A fourth guide is that, in the case of partial ownership 
of wealth, the aggregate of all the partial rights constitutes 
the total ownership. We may picture to ourselves all ar- 
ticles of wealth as having attached to them streams of 
services stretching out into the future. These services 
are cut up among separate owners in different ways, some- 
times transversely, sometimes longitudinally, and some- 
times definite parts of them are separated out. The total 
ownership of the wealth is simply the aggregate of the rights 
to the entire stream of future services. It may, of course, 
be true that the character and size of this stream of services 
will differ according to the different methods by which 
its ownership is parceled out. This fact, however, does 
not invalidate the principle that the total ownership is 
the combination of all the partial rights. 

In common speech the minor rights to wealth are not 
ordinarily dignified as rights of ownership. Thus, a ten- 
ant's right in the dwelling he occupies is sharply distin- 
guished from the right of the owner. Yet the law recog- 
nizes a leasehold as an estate in the land, and when the 



Sec. 9] PROPERTY 35 

owner of land wishes to sell and convey an unencumbered 
fee simple title, he finds it necessary to extinguish all out- 
standing leases, or claims for future services, often at con- 
siderable cost. Recently the New York Reform Club 
sold its leasehold in a building for $25,000, because the pur- 
chaser could not afford to wait for the expiration of the 
lease. The total ownership always includes the ownership 
of the tenant. 

In like manner, the total value of any concrete wealth 
is the total value of the property rights in it. The close 
correspondence between wealth and property gives us a 
new method of appraising wealth, namely, by appraising 
the property rights to it. In fact, we are here provided 
with another sense of appraisement of wealth, in addition 
to the several already given in Chapter I, Such appraise- 
ment may mean, not what the whole article of wealth 
would sell for en bloc, but the sum of the values of the par- 
tial rights to it when these latter are appraised on the basis 
of small individual sales. Thus, the value of a railroad, 
operating under normal conditions, is found by taking the 
sum of the values of its stocks and bonds. Railways are 
seldom sold as a whole, but their stocks and bonds are 
constantly on the market, and are often the only means of 
affording a valuation. 

It is true that under these circumstances the market price 
of the stock would form no basis for judging what would 
be the value of the road if sold as a whole. There would 
need to be added the value of "control." But this will 
be accounted for by an addition to the value of such of the 
shares as will secure this control. "Control" is the power, 
coming from a majority of votes, to obtain from the road 
some services which would not be possible without such 
majority ownership. The additional benefit thus obtained 
may be illegitimate, as when the parties in control vote 
themselves large salaries. But whether legitimate or ille- 
gitimate, the power to make the road better serve one's 



36 NATURE OF CAPITAL AND INCOME [Chap. II 

interest often affects profoundly the value of the shares. 
The stock of the Chicago, Burlington, and Quincy Railroad 
was quoted at $132 when a certain capitalist determined to 
buy it. Knowing that it would be almost impossible to 
acquire all the stock by ordinary means, he offered instead 
to take over as much as should be offered to him, provided 
it was more than half, and to give $200 in four per-cent 
bonds for each $100 share, — an offer which was accepted by 
most of the stockholders. The acceptance added at once 
fifty per cent to the market value of the stock, and improved 
even the value of the bonds ; so that the value of the system, 
sold virtually as a whole, was much more than of the stock 
and bonds before the negotiation was opened. The valua- 
tion of the road will thus be different according to whether 
it is under the control of a particular interest or whether 
its ownership is widely distributed, as well as according to 
the purpose for which the valuation is made.^ But in every 
instance the value of the railroad is the sum of the values 
of the complete aggregate of rights in it. 

If one bears in mind the explanations which have been 
given, there can scarcely be any difficulty in tracing out for 
each property right some underlying wealth, so that we may 
give adherence to the general principle that wealth and prop- 
erty are coextensive. That this is true as a "general fact" 
cannot fail to be admitted even were it necessary to reject 
it as a "necessary truth." But if our definitions of wealth 
and property are adopted, it becomes also a necessary truth. 

§10 
Having seen what property is, we may now classify 
property rights. There are two chief classes, complete 
rights and partial rights. A complete, or practically 
complete, right, or "fee simple" to an article of wealth, is a 
right to all those uses of that article which are owned; a 

^ The completest account of railway valuation is that contained 
in Bulletin 21, "The Commercial Valuation of Railway Operating 
Property," United States Census, 1905. 



Sec. 10] 



PROPERTY 



37 



partial right is a right to a part of its uses. The partial 
rights are the only ones which make difficulty. 

The services of an article of wealth may be apportioned 
among different part owners in many ways. If they are 
divided longitudinally in time, the rights of the various 
coowners are similar to each other. The chief examples 
are the rights of partners and stockholders, and the less 
well-defined rights of the individual members of a club, 
family, or commune to the common property and all rights 
in common, and, finally, the rights to the different kinds of 
uses, as, for instance, where one person owns the right of 
farming a piece of land, another the right of mining its 
minerals, and a third the right of fishing in the streams 
which run through it. 

If the services are divided transversely in time, one per- 
son has the rights of all services up to a particular date, 
and another all the rights beyond that. The former 
person is called the tenant and the latter the landlord. 

If the services are Hmited both in time and also in quantity 
or value, we have still another group of property rights. 
These and other classes are seen in the following scheme 
of classification. 

Complete (Fee Simple) 

to services cut longitudinally 



Ph 
O 



. Partial 



to services cut transversely 



rights to definite parts 
of services 



r rights in common 
rights to different 

-i usufructs 
partnership rights 
joint stock shares 

(lease 
reversion 
patent and copyright 

(bonds 
private notes 
banknotes 
bank deposits 

(checks, drafts, and 
bills of exchange 
irredeemable paper 
money 



orders 



..,„., f good will and custom 
, mmor and mdennite < ° . 

[ taxmg power 



38 NATURE OF CAPITAL AND INCOME [Chap. II 

§11 

Since wealth and property are each the opposite aspect 
of the other, economics might be described as the "sci- 
ence of property" quite as truly as the "science of wealth." 
If we are studying the economic condition of a whole 
country, we prefer to fix our attention upon wealth, caring 
less about how its ownership is divided. We are then inter- 
ested in the acreage of wheat fields, the extent of coal 
mines, railways, factories, and homesteads, and not in their 
owners. On the other hand, if we are studying the "dis- 
tribution of wealth" — the condition of individuals or of 
classes — it is property on which we need to fix attention. 
The idea of wealth, therefore, is associated with the wel- 
fare of the community in general, while that of property 
is associated with the welfare of the different individuals 
in the community. 

But, it may be asked, why is so much stress laid on 
the principle that wealth and property are coextensive? 
It may be conceded that most of the principles of political 
economy will be unaffected whether or not this one is ac- 
cepted as rigorously true. Its usefulness consists in help- 
ing us to arrange our ideas. At present there seems to 
exist in the popular mind a confusion of the concepts of 
wealth, property, certificates of property, services, and utihty, 
all of which should be carefully separated from each other. 
No one can fully understand monetary problems, for instance, 
unless he distinguishes carefully the three elements to which 
the term "money" is indiscriminately applied. There is 
raonej-wealth, such as a gold eagle; money-property, such 
as the right of a holder of "greenbacks"; and money-cer- 
tificates, such as the paper "greenbacks" themselves. If 
the fact that wealth and property are coextensive were more 
generally known and acknowledged, some very practical and 
salutary results would follow. Wild schemes of currency 
inflation, which are based on the idea that wealth may be 



Sec. 11] PROPERTY 39 

increased simply by multiplying the titles to it, would be 
checked, and the usual atrocities of double taxation, for in- 
stance, of farm and mortgage, or of railways and railway 
shares, would be avoided/ 

If we bear in mind the distinctions in this and in the 
previous chapter, we shall see that there is no advantage, 
but much disadvantage, in including any "immaterial" 
elements in wealth. "Immaterial wealth" is, in fact, one 
of those bugaboos which have done a great deal to obscure 
the simplicity of economic relations. Legal advice or 
medical attendance are not "immaterial wealth" ; they are, 
as we have seen, simply services of wealth (human wealth 
in this case). The "properties and powers of nature" 
are not wealth, but, as explained in the previous chapter, 
are attributes of land and enter economic science merely 
as giving characterization to that particular kind of wealth. 
They cannot be counted as wealth in addition to the land 
any more properly than can the elasticity of rubber be 
counted as wealth in addition to the rubber. Likewise, 
swift horses are wealth, but not their swiftness ; honest, wise, 
successful, and healthy men are wealth, but not their hon- 
esty, wisdom, skill, or health. Most of the mystery of 
banking to the ordinary mind consists in the mistaken no- 
tion that credit is something "inflated," without a tangible 
basis. A mere inspection of a bank's balance sheet should 
serve to make clear the fact that behind every claim upon 
the bank is something to make it good. If the anterior 
something be itself a claim on some other bank or person, 
there lies behind it, in turn, some basis, and so on until a 
concrete instrument is finally found. 

Another common error is the belief that "wealth con- 
sists of utility." If this were true, the law of diminishing 

^ See Report of Professor Edward W. Bemis and Carl H. Nau, on 
Value of Ohio Railroads, 1903; also, Report of the Interstate Com- 
merce Commission on Railways in the United States in 1902, 1903, 
Part V. 



40 NATURE OF CAPITAL AND INCOME [Chap. II 

utility, that equal increments of wealth have decreasing 
increments of utility, would be a contradiction in terms. 

To plead in extenuation of such confusions the fact that 
popular usage is guilty of them, is like trying to justify in 
the science of physics a jumbling together of the concepts 
of mass and density, or of velocity and acceleration, or of 
force and energy, on the ground that the ordinary man does 
not distinguish between them. The proper method of 
avoiding large errors in any science is to avoid small ones 
at the outset. This can be accomplished only by scrupu- 
lous attention to elementary distinctions. 



CHAPTER III 

UTILITY 



We have seen that all wealth and property imply pro- 
spective services or "desirable events." It is the desir- 
ability of these future expected services which gives meaning 
to all economic phenomena. It would therefore be im- 
possible, in any full view of the subject, to confine our- 
selves strictly to the study of objective wealth, property, 
and services. In the present chapter we shall consider 
briefly the subjective or psychical element in economics. 

Wealth is wealth only because of its services ; and serv- 
ices are services only because of their desirability in the 
mind of man, and of the satisfactions which man expects 
them to render. Indeed, the desirability of services is 
implied in their very definition as "desirable events." 
The mind of man supplies the mainspring in the whole eco- 
nomic machinery. It is in his mind that desires originate, 
and in his mind that the train of events which he sets 
going in nature comes to an end in the experience of sub- 
jective satisfactions. It is only in the interim between the 
initial desire and the final satisfaction that wealth and its 
services have place as intermediaries. 

We are thus led to consider two. new concepts, — that 
of " desirability " and that of " satisfaction." Both of 
these enter into our consideration only as they are applied 
to the three economic elements, — wealth, property, 
services. To avoid unnecessary repetitions, we may treat 
these three elements under the one rubric of "goods." 

41 



42 NATURE OF CAPITAL AND INCOME [Chap. Ill 

§2 

The desirahility, then, of any particular goods, at any 
particular time, to any particular individual, under any 
particular conditions, is the strength or intensity of his de- 
sire for those goods at that time and under those conditions. 
What is here called desirability is identical with what has 
usually been called in economic writings "utihty." But 
utility, though not to be utterly displaced, is not the hap- 
piest term for our purpose. To say nothing of the mere 
awkwardness of its only antithetical term — "disutility" 
— as compared with "undesirability," it has fallen heir 
to so many different meanings that its use here is apt to 
be confusing. The term "useful," for instance, in ordinary 
language is employed in opposition to "ornamental." 
In this sense diamonds are said to be ornamental and not 
useful, though in economic science they are adjudged 
useful. Again, "utility" usually imphes intrinsic merit, 
whereas, when we employ it in economic science, we are 
obliged to apply it to any noxious thing considered by its 
owner desirable, for instance, opium, alcohol, or degrad- 
ing literature. Finally, in the last few years, the word 
"utility" has come into a new and technical meaning as 
employed in the phrase "public utilities," which desig- 
nates electric lighting plants, street railway systems, gas 
works, and many other things which are merely collections 
of wealth of a peculiar kind. 

In order to obviate these objections, Professor Pareto 
has proposed an entirely new term, "ophelimity." This 
has both the advantages and the disadvantages of any 
newly invented technical term, and has thus far shared 
the fate which usually befalls the attempt to coin words. 
The word "utility" is still employed, and it is not likely 
that "desirability," "ophelimity," or any other term will 
soon displace it. In the present book we shall use both 
"utility" and "desirability," but preferably the latter. 



Sec. 3] UTILITY 43 

In proposing that economists substitute so far as possible 
the term " desirabihty " for '^utihty/' the author is simply 
following the example of Professor Gide ^ and Professor 
Marshall. 

§ 3 

If the term "utility" is to be used at all, we must dis- 
tinguish the utihty of goods from the use of the goods. 
As has been pointed out, the uses or services of goods are 
the desirable events which occur by their means. Utihty, 
on the other hand, is not these desirable events, but their 
desirability. 

Again, the desirabihty or utility of goods must not be 
confused with the pleasure which may be ultimately ob- 
tained from those goods. Here our second concept is 
involved, for pleasure is not the desire, but the satisfac- 
tion of the desire. It is an experience in time, and requires 
duration of time for its existence. Desirability, which 
means the intensity of desire of an individual under certain 
conditions, merely indicates a state of mind at a particular 
point of time, namely, the point of time at which he mentally 
weighs and measures the desirability of any contemplated 
service, property, or wealth. We may speak of the de- 
sirability of a fruit orchard to a particular person on Janu- 
ary 1, 1905; but the pleasure derivable from that orchard 
is only to be experienced during future years, as it bears 
fruit and the fruit gives enjoyment to those who eat it. 
Thus we have two concepts : utility or desirability, — a 
state of mind at a point of time ; and pleasure or satisfac- 
tion, — an experience of mind through a period of time. 
These two concepts are closely related ; for the desirabihty 
of goods is simply the present esteem in which the future 

1 Gide's Principles of Political Economy, 2d American ed., 1904, 
p. 48. See also the present writer's " Mathematical Investigations in the 
Theory of Value and Prices," Transactions of the Connecticut Academy, 
1892, p. 23. 



44 NATURE OF CAPITAL AND INCOME [Chap. Ill 

satisfactions from those goods are held. But the two are 
none the less distinct. It is with utihty or desirability 
that we are concerned in this chapter. 



The desirability of any particular goods may relate to 
the whole or to any part of the group of goods. The de- 
sirability of the entire group is called the total desirability ; 
the desirability of one unit more or less of the group is 
called the marginal desirabihty. In economic science we 
have to do more with marginal than with total desirability, 
and it is important that the concept of marginal desir- 
ability should be thoroughly understood. 

That marginal desirability is the desirabihty of one unit, 
more or less, may be illustrated as follows: If a person 
possesses ten chairs, their marginal desirabihty is the differ- 
ence, in his mind, between the desirabihty of having ten 
chairs and the desirabihty of having nine chairs; that is, 
it is the desirability sacrificed by having one chair less. 
Or, what is almost the same thing, the marginal desirabihty 
of the group of ten chairs is the desirability of one chair 
more, — the difference in desirability between eleven chairs 
and ten. Whether the marginal desirabihty is taken as 
referring to one unit more or to one unit less is usually of 
so httle importance as not to require separate designations 
to distinguish them, and in case the commodity is one which 
admits of indefinite subdivision, as flour, wheat, coal, etc., 
the two coalesce as the size of the increment is reduced in- 
definitely.^ This fact is usually expressed by saying that 
the marginal desirability of the chairs is the desirabihty of 
"the tenth" chair. But though this mode of statement is 
correct, it is not intended to convey the idea that any par- 
ticular chair is the "tenth" chair. 

The group of goods the marginal desirabihty of which is 
under consideration may be any specified group of goods 

1 For a mathematical treatment see Appendix to Chap. Ill, § 1. 



Sec. 4] UTILITY 45 

whatever. Reference may be had to a specified group of 
goods now existing, or to a specified group of goods in the 
future, or to a specified flow of goods through a period of 
time. For instance, the marginal desirabiHty of coal to an 
individual may be taken to refer to the particular stock of 
coal in his bin at the present moment. If this stock con- 
sists of fifteen tons, its marginal desirability is the desir- 
ability of the fifteenth ton, or the difference to him between 
the desirability of having fifteen and that of having four- 
teen tons. Or, reference may be had to an intended pur- 
chase of coal to be delivered in three months. If we con- 
sider a possible purchase of future coal to the extent of 
fifteen tons, its marginal desirability then represents the 
present desire for the fifteenth ton, in exactly the same 
way as though reference were had to an existing stock. 
Again, if a person is consuming in his household fifteen tons 
of coal a year, its marginal desirability at any instant is 
the desirability of the fifteenth ton, or the sacrifice which 
would be occasioned were he to reduce his yearly consump- 
tion from fifteen tons to fourteen. 

Again, the group of goods considered may consist of ar- 
ticles all of which are of the same kind, or of a heterogeneous 
collection. In the preceding examples the goods were of 
exactly the same kind. As an example of the marginal 
desirability of a group consisting of diverse kinds, we 
may cite the desirability of an additional monthly magazine 
or newspaper. If a subscriber is already taking ten periodi- 
cals of different kinds, the desirabiHty of a specified journal 
additional to the existing assortment may be regarded as 
the marginal desirability with reference to the entire group 
of journals. 

In the same way we may speak of the marginal desir- 
ability of a series of characteristics or features connected with 
any article or articles of wealth. A person contemplating 
the building of a house may have to decide how many win- 
dows he will put in. If he contemplates fifty windows, the 



46 NATURE OF CAPITAL AND INCOME [Chap. Ill 

marginal desirability of the windows is the desirability of 
the fiftieth window, or the difference in the desirability 
of having fifty windows rather than forty-nine. 

§5 

The first principle in regard to marginal desirability 
is that an increase in the quantity of goods in the group 
the marginal desirabihty of which is under consideration, 
results in a decrease in the marginal desirability of the 
group. Each successive increment is less desirable than 
the preceding increment. The marginal desirability of 
sugar to the householder consuming five pounds weekly is 
greater than the marginal desirability if six pounds are con- 
sumed, and is successively diminished as each successive 
pound is added to his consumption. 

It is well to remember that when the term "successively" 
is here employed, it is not used in a temporal sense. The 
succession to which it refers is not a succession in time, but 
a succession in thought. We consider the consumer of 
sugar under a series of different hypotheses which we 
examine successively. We begin with the hypothesis of 
a weekly consumption of five pounds, and take up succes- 
sively the hypotheses of six pounds, seven pounds, eight 
pounds, etc. The desirabihty of the "last" pound in this 
series is the marginal desirability for the group ending at 
that point; but the "last" pound refers to the one consid- 
ered last in our mental review, and not the one acquired last 
by the consumer. This fact needs to be emphasized, in 
view of frequent confusion on the subject occasioned by too 
loose an employment of the words "last" and "successive." 
It is presumably because of the time confusions involved 
in these words that, under the leadership of Wieser^ and 
Marshall,^ economists have substituted the phrase "mar- 
ginal utihty " for the older phrase of Jevons, "final utility." 

With these provisos and explanations in view, it is clear 

^ Ursprung des Werthes, p. 128. 

2 Principles of Economics, 3d ed., 1895, p. 168. 



Sec. 5] UTILITY 47 

that the total desirability of any group of goods is the sum 
of the desirabilities of the successive units. The total 
desirability of the ten chairs, for instance, is found by add- 
ing together (1) the desirability of having only one chair, 
(2) the desirability of having a second chair, (3) a third, 
(4) a fourth, etc., until ten chairs have been considered. 
These successive desirabilities will evidently continually 
diminish. Hence their sum, or the total desirability of the 
group, is not the same thing as ten times the marginal de- 
sirability. In this is found the explanation of the fact that 
the possessor of the chairs regards them as possessing much 
more total desirability to him than the total desirability 
of the money which they cost, although the loss of any one 
of the ten chairs may not represent more desirability than 
the desirability of the money which that one chair cost.^ 

As is well known to all students of the modern theory 
of value, marginal desirability lies at the root of the deter- 
mination of value and price. We are here concerned, 
however, not in applying the concept of marginal desir- 
ability to the determination of economic magnitudes, but 
merely in explaining its nature. 

Although the definitions which have been given of de- 
sirability serve to explain its nature, they do not enable 
us to employ it in a quantitative manner. The exact 
measurement of desirability is a subject of much impor- 
tance, as well as of great difficulty. Inasmuch as in the 
present work only an incidental use will be made of these 
concepts, it does not seem proper here to enter into these 
discussions.^ 

^ Cf. Fetter's Principles of Economics, New York, 1904, pp. 25-26. 

^ See the writer's " Mathematical Investigations in the Theory of 
Value and Prices," Transactions of the Connecticut Academy of Arts 
and Sciences, 1893, Vol. IX; Pigou, Economic Journal, March, 1903, 
Vol. XIII; Pareto, Cours d' Economic Politique, Vol. I; Giornale 
d'Economisti, August, 1892; J. B. Clark, "Ultimate Standard of 
Value," Yale Review, November, 1892; Seligman, Principles of 
Economics, Longmans, Green & Co., 1905, Chap. XIII; Chin tao 
Chen's Societary Circulation, a doctor's thesis, Yale Univ., 1906. 



PART I. Capital 

Chapter IV. Capital 

Chapter V. Capital Accounts 

Chapter VI. Capital Summation 



CHAPTER IV 

CAPITAL 



In the foregoing introduction we have set forth several 
fundamental concepts of economic science, — wealth, 
property, services, satisfactions, utility, price, and value. 
We have seen that wealth consists of material appropriated 
objects, and property, of rights in these objects ; that wealth 
in its broadest sense includes human beings, and property 
in its broadest sense includes all rights whatsoever; that 
services are the benefits of wealth, satisfactions the enjoy- 
ment of services, and desirability or utility the desire for 
wealth, property, services, or satisfactions; that prices are 
the ratios of exchange between quantities of wealth, prop- 
erty, or services ; and, finally, that value is the price of any 
of these multiplied by the quantity. These concepts are 
the chief tools needed in economic study. 

Nothing has yet been said as to the relation of these 
various magnitudes to that great " independent variable " 
of human experience, time. When we speak of a certain 
quantity of wealth we may have reference either to a quan- 
tity existing at a particular instant of time, or to a quan- 
tity produced, consumed, exchanged, or transported during 
a period of time. The first quantity is a stock (or fund) 
of wealth; the second quantity is a flow (or stream) of 
wealth. The contents of a granary at noon, January 1, 
1906, is a stock of wheat ; the amount of wheat which has 
been hoisted into it during a week, or the amount of wheat 
which has been exported from the port of New York during 

51 



V 



52 NATURE OF CAPITAL AND INCOME [Chap. IV 

1905, is a flow of wheat. The term "wealth" by itself is 
insufficient to determine which of these two kinds of mag- 
nitudes is meant. Similarly, when we speak of property 
or of value, we may have in mind either a fund or a flow. 
A thousand shares in a certain company owned by a cer- 
tain man at a certain time constitute a particular fund of 
property ; the number of shares transferred in a week on the 
stock exchange constitute a flow of property. Again, the 
value of the checks held at noon of any day by one bank 
drawn on other banks constitutes a fund of value ; the value 
of the checks which pass through a clearing-house in twenty- 
four hours constitutes a flow of value. Services and satis- 
factions, unUke wealth and property, can exist only as 
flows ; a fund of either is impossible. 

A fund is fully specified by one magnitude only ; a flow 
requires two, — the amount of flow and the duration of flow. 
From these two a third follows, — the rate of flow or the 
quotient of the amount divided by the duration. The rate 
of flow is often of more importance than the amount of flow. 
Thus we care less to know the aggregate wages of a work- 
man during a fifetime than the rate of his wages during 
various periods of his fife. 

The distinction between a fund and a flow has many 
applications in economic science.^ The most important ap- 
pfication is to differentiate between capital and income. 
Capital is a fund and income a flow. This difference be- 
tween capital and income is, however, not the only one. 
There is another important difference, namely, that capital 
is wealth, and income is the service of wealth. We have 
therefore the following definitions: A stock of wealth ex- 
isting at an instant of time is called capital. A flow of serv- 
ices through a period of time is called income. Thus, a 
dwelling house now existing is capital ; the shelter it affords 
or the bringing in of a money-rent is its income. 

1 For some of these applications, e.g. to monetary circulation, see: 
" What is Capital ? " Economic Journal, 1897. 



Sec. 2] CAPITAL 53 

The railways of the country are capital ; their services of 
transportation or the dividends from the sale of that 
transportation are the income they yield. 

The distinction between capital and income is somewhat 
analogous to the distinction between desirability and satis- 
factions, which was emphasized in Chapter III ; for desira- 
bility was shown to relate to a point of time and satisfactions 
to a period of time. 

§2 

The foregoing definitions of capital and income are not, 
it is true, universally accepted. Many authors attempt 
to define capital, not as wealth in a particular as- 
pect with reference to time, but as a particular kind or 
species of wealth, or as wealth restricted to a particular 
purpose; in short, as some specific part of wealth instead 
of any or all of it. We are obliged, therefore, to pause a 
moment to consider these opinions. In this chapter 
we are concerned with the concept of capital only. 

From the time of Adam Smith it has been asserted 
by economists, though not usually by business men, 
that only particular kinds of wealth could be capital, and 
the burning question has been, What kinds ? But the fail- 
ure to agree on any dividing hne between wealth which is 
and wealth which is not capital, after a century and a half 
of discussion, certainly suggests the suspicion that no 
such hne exists.^ What Senior wrote seven decades ago 
is true to-day: "Capital has been so variously defined, 
that it may be doubtful whether it have any generally 
received meaning."^ In consequence, "almost every 
year there appears some new attempt to settle the disputed 
conception, but, unfortunately, no authoritative result 
has as yet followed these attempts. On the contrary, 

^ For a fuller statement than that which follows of the dis- 
agreements and confusions on this subject, see the writer's "What is 
Capital?" Economic Journal, December, 1896. 

^ "Political Economy," Encyclopcedia MetropoUtana, Vol. VI, p, 153. 



54 NATURE OF CAPITAL AND INCOME [Chap. IV 

many of them only served to put more combatants in the 
field and furnish more matter to the dispute."^ Many 
authors express dissatisfaction with their own treatment 
of capital, and even recast it in successive editions.^ 

Adam Smith's ^ concept of capital is wealth which 
3delds "revenue." He would therefore exclude a dwelling 
occupied by the owner. Hermann/ on the other hand, 
includes dwelUngs, on the ground that they are durable 
goods. But a fruiterer's stock in trade, which is capital 
according to Smith, because used for profit, according to 
Hermann does not seem to be capital, because it is perish- 
able. Knies ^ calls capital any wealth, whether durable or 
not, so long as it is reserved for future use. Walras ^ 
attempts to settle the question of durabihty or futurity 
by counting the uses. Any wealth which serves more than 
one use is capital. A can of preserved fruit is therefore 
capital to Knies if stored away for the future, but is not 
capital to Walras because it will perish by a single use. 
To Kleinwachter,^ capital consists only of "tools" of pro- 
duction, such as railways. He excludes food, for instance, 
as passive. Jevons,^ on the contrary, makes food the most 
typical capital of all, and excludes railways, except as rep- 
resenting the food and sustenance of the laborers who built 
them. 

While most authors make the distinction between capital 
and non-capital depend on the kind of wealth, objectively 
considered. Mill ^ makes it depend on the intention in the 
mind of the capitalist as to how he shall use his wealth, 

1 Bohm-Bawerk, Positive Theory of Capital, English translation, 
London and New York, 1891, p. 23. 

2 E.g. Roscher, Marshall, Schaffle. 

3 Wealth of Nations, Book II, Chap. I. 

* Staaiswirtschaftliche Untersuchungen, Munich, 1832, p. 59. 
5 Das Geld, 2d ed., Berhn, 1885, pp. 69-70. 

' Elements d'Economie Politique Pure, 4th ed., Lausanne, p. 177. 

'' Grundlagen des Socialismus, 1885, p. 184. 

» Theory of Political Economy, 3d ed., 1888, Chap. VII, pp. 222, 242. 

* Principles of Political Economy, Book I, Chap. IV, § 1. 



Sec. 2] CAPITAL 55 

Marx ^ makes it depend on the effect of the wealth on the 
laborer, and Tuttle,^ upon the amount of wealth possessed. 
Again, while most authors confine the concept of capital 
to material goods, MacLeod^ extends it to all immaterial 
goods which produce profit, including workmen's labor, 
credit, and what he styles "incorporeal estates," such as 
the Law, the Church, Literature, Art, Education, an au- 
thor's Mind. Clark ^ takes what he styles "pure" capital 
out of the material realm entirely, making it consist, not 
of things, but of their utiHty. Most authors leave no place, 
in their concept of capital, for the value of goods as distinct 
from the concrete goods themselves, whereas Fetter,^ in his 
definition, leaves place for nothing else. Some definitions 
are framed with especial reference to particular problem^s 
of capital; many, for instance, have reference to the prob- 
lem of capital and labor, but they fail to agree as to the re- 
lation of capital to that problem. MacCuUoch ® regards it 
as a means of supporting laborers by a wage fund ; Marx,^ 
as a means of humiliating and exploiting them ; Ricardo,^ 
as a labor saver; MacLeod,^ as including labor itself as 
a special form of capital. 

Many definitions have reference to the problem of 
production, but in no less discordant ways. Accord- 
ing to Senior,^ Mill,® and many others, capital must be 
itself a product. Walras,*" MacLeod,^ and others admit 

^ Capital, English translation, London, 1887, Vol. II, p. 792. 
^ "The Real Capital Concept," Quarterly Journal of Economics 
November, 1903. 

^ Dictionary of Political Economy, article "Capital," p. 331. 

* Capital and its Earnings, Publications of American Economic 
Association, 1888, pp. 11-13. 

^ "Recent Discussion of the Capital Concept," Quarterly Journal of 
Economics, November, 1900, and Principles of Economics, 1904. 
^ Principles of Political Economy, 4th ed., p. 100. 
' Principles of Political Economy, § 37. 

* "Political Economy," Encyclopaedia Metropolitana, Vol. VI, p. 
153. 

^ Principles of Political Economy, Book I, Chap. IV, § 1. 

^° Elements d'^conomie Politique Pure, Lausanne, 4th ed., p. 177. 



56 NATUKE OF CAPITAL AND INCOME [Chap. IV 

land ^ and all natural agents under capital. Bohm-Bawerk,^ 
while agreeing that it must be a product, insists that it 
must not apply to a finished product. Marx ^ denies that 
capital is productive. Bohm-Bawerk ^ admits that it is 
not "independently" productive, but denies the Marxian 
corollary that it should not receive interest. Other writers 
make it coordinate with land and labor as a productive 
element. 

As to what it is that capital produces there is further 
disagreement. Adam Smith ^ affirms that capital produces 
"revenue," Senior,^ that it produces "wealth." Others 
vaguely imply that it produces value, services, or utiUty. 

Most of the definitions involve some reference to time, 
but in many different ways. Hermann ^ has in mind the 
time the wealth will last; Clark,^ the permanency of the 
fund capital as contrasted with the transitoriness of its 

1 The fancied distinction between land and capital, viz., that the 
former yields rent and the latter interest, and that rent varies with 
different grades of land whereas interest is uniform for all sorts of 
capital, is based on a confusion between quantity and value of wealth. 
The return from land per acre will, it is true,' vary according to the 
quality of the land. But so also the return from machinery of differ- 
ent grades will vary per machine. The return from different kinds of 
capital per $100 worth will, it is true, be uniform; but so will the 
return from land per $100 worth. For a full treatment of this confu- 
sion see Fetter's "The Relations between Rent and Interest," a paper 
presented before the American Economic Association, December, 1903. 
Cf. Clark, Capital and its Earnings, p. 27, and Distribution of Wealth 
(Macmillan, 1899), Chaps. IX and XIII. Cannan developed the same 
idea in " What is Capital ? " Economic Journal, June, 1897. Cf . the 
writer's " R61e of Capital," Economic Journal, December, 1897, pp. 524, 
526. 

2 Positive Theory of Capital, Enghsh translation, London and New 
York, 1891, p. 38. 

3 Capital, Enghsh translation, London, 1887, Vol. II, p. 792. 

* Capital and Interest, Book VI. « 

^ Wealth of Nations, Book II, Chap. I. 

^ "Political Economy," Encyclopcedia Metropolitana, Vol. VI, p. 
153. 

' Staatswirtschaftliche Vntersuchungen, Munich, 1832, p. 59. 

8 Capital and its Earnings, PubUcations of American Economic 
Association, 1888, pp. 11-13. 



Sec. 3] CAPITAL 57 

elements, "capital goods"; Knies/ the futurity of satis- 
factions; Jevons/ and Landry/ specifically the time be- 
tween the "investment" of the capital and its return. 

§3 

It is idle to attempt any reconcihation between concepts 
of capital so conflicting, and yet there are elements of 
truth in all. Though generally wrongly and narrowly 
interpreted, there are certain recurrent ideas which are 
entirely correct. The definitions concur in striving to ex- 
press the important facts that capital is productive, that it 
is antithetical to income, that it is a provision for the future, 
or that it is a reserve. But they assume that only a part of 
all wealth can conform to these conditions. To the authors 
of the definitions quoted, it would seem absurd to include all 
wealth as capital, as there would be nothing left with which 
to contrast it and by which to define it. And yet, as 
Professor Marshall says, when one attempts to draw a 
hard-and-fast line between wealth which is capital and 
wealth which is not capital, he finds himself "on an in- 
chned plane," constantly tending, by being more Hberal 
in his interpretation of terms, to include more and more in 
the term capital, until there is little or nothing left outside 
of it. We are told, for instance, that capital is "wealth 
for future use." But "future" is an elastic term. As was 
shown in Chapter II, all wealth is, strictly speaking, for 
future use. It is impossible to push back its use into the 
past; neither is it possible to confine it to the present. 
The present is but an instant of time, and all use of wealth 
requires some duration of time. A plateful of food, how- 
ever hurriedly it is being eaten, is still for future use, though 
the future is but the next few seconds; and if by "future" 
we mean to exclude the "immediate future," where is the 

1 Das Geld, 2d ed., 1885, pp. 69-70. 

^ Theory of Political Economy, 3d ed., 1888, Chap. VII, pp. 222-242. 

^ L'Interet du Capital, Paris (Giard), 1904, p. 16. 



58 NATURE OF CAPITAL AND INCOME [Chap. IV 

line to be drawn ? Are we to say, for instance, that capital 
is that wealth whose use extends beyond seventeen days ? 

And as all wealth is for future use it is also, by the same 
token, all a "reserve." To call capital a reserve does not, 
therefore, in strictness, delimit it from other wealth. Even 
a beggar's crust in his pocket will tide him over a few hours.^ 

Equally futile is any attempt definitely to mark off 
capital as that wealth which is "productive." We have 
seen that all wealth is productive in the sense that it yields 
services. There was a time when the question was hotly 
debated what labor was productive and what unproductive. 
The distinction was barren and came to be so recognized. 
No one now objects to calHng all labor productive. And 
if this productivity is common to all labor, it is equally 
common to all wealth. If we admit that a private coach- 
man is a productive worker, how can we deny that the 
horse and carriage are also productive, especially as the 
three merely cooperate in rendering the very same service, 
— transportation ? 

Finally, we cannot distinguish capital as that wealth 
which bears income. All wealth bears income, for income 
consists simply of the services of wealth. But the idea 
that some wealth bears income and some not has been per- 
sistent from the time of Adam Smith, who, meaning by in- 
come only money income, conceived capital as the wealth 
which produces income in this sense, as distinguished from 
the wealth, such as dwellings, equipages, clothing, and food, 
which dissipates that income. A home, according to him, 
is not a source of income, but of expense, and therefore can- 
not be capital, 

§4 

In these and other ways have economists introduced, in 
place of the fundamental distinctions between fund and flow, 
and between wealth and services, the merely relative dis- 

1 See the writer's "Precedents for Defining Capital," Quarterly 
Journal of Economics, May, 1904, p. 404. 



Sec. 4] CAPITAL 59 

tinction between one kind of wealth and another. As a 
consequence, their studies of the problems of capital have 
been full of confusion. Among the many confusions ^ 
which have come from overlooking the time distinction 
between a stock and a flow was the famous wage fund 
theory, that the rate of wages varies inversely with the 
amount of capital in the supposed "wage fund." Mac- 
Culloch wrote : ^ — 

" To illustrate this principle, let us suppose that the capital of a 
country appropriated to the payment of wages would, if reduced to 
the standard of wheat, form a mass of 10,000,000 quarters; if the 
number of laborers in that country were two millions, it is evident 
that the wages of each, reducing them all to the same common 
standard, would be five quarters." 

"The wages would be five quarters" — thus MacCul- 
loch — but five quarters in what time ? Five quarters per 
hour, per day, or per year ? Divorced as it is from any time 
concept, this definition is meaningless. 

Even so acute a writer as John Stuart Mill unhesitatingly 
states : ^ — 

"Wages, then, depend mainly upon the demand and supply of 
labour; or, as it is often expressed, on the proportion between popu- 
lation and capital. By population is here meant the number only 
of the labouring class, or rather of those who work for hire ; and by 
capital, only circulating capital, and not even the whole of that, but 
the part which is expended in the direct purchase of labour. To this, 
however, must be added all funds which, without forming a part of 
capital, are paid in exchange for labour, such as the wages of soldiers, 
domestic servants, and all other unproductive labourers. . . . With 
these limitations of the terms, wages not only depend upon the rela- 
tive amount of capital and population, but cannot under the rule of 
competition be affected by anything else. Wages (meaning, of course, 
the general rate [sic]). ..." 

A httle attention to business bookkeeping would have 
saved economists from such errors ; for the keeping of rec- 
ords in business involves a practical if unconscious recog- 

1 See "What is Capital?" loc. cit. 

2 Principles of Political Economy, 1st ed., pp. 327-328, 2d ed., pp. 
377-378. See Cannan, History of Theories of Production and Distri- 
bution, p. 264. 

^ Political Economy, Book II, Chap. XI, § 1. 



60 NATURE OF CAPITAL AND INCOME [Chap. IV 

nition of the time principle here propounded. The "capi- 
tal account" of a railway, for instance, gives the condition 
of the railway at a particular instant of time, and the "in- 
come account" gives its operation through a period of time. 

§5 

It has been objected that the proposed definition does 
not conform to established usage. So far as economic prece- 
dent is concerned, we have already seen that there is no 
established usage.^ Moreover, in the immense Uterature 
on the subject there is no lack of precedent for the defini- 
tion here proposed. Turgot ^ employed the term capital 
in practically the sense of a stock of wealth. J. B. Say,^ 
Courcelle-Seneuil,^ and Guyot ^ followed. Edwin Cannan,^ 
among present economists, reintroduced it, and in a very 
clear and explicit way. To-day it is used in five or six 
standard works,^ as well as in some minor writings. Many 
economists have orally expressed their approval of the pro- 
posed definition. 

Others virtually or approximately adopt it, as, for in- 
stance, Knies,« Clark,« Pareto,' Giffen,^ De Foville," Flux,^^ 

1 For a fuller statement of this fact see the writer's "Precedents 
for Defining Capital," Quarterly Journal of Economics, May, 1904. 

2 Formation and Distribution of Riches, § 58, Ashley's translation 
(Macmillan, New York), pp. 50-59. 

^ See Tuttle, "The Real Capital Concept," Quarterly Journal of 
Economics, November, 1903, p. 83; but of. Bohm-Bawerk, Positive 
Theory, English translation, p. 59, n. 

* Traite theorique et pratique d' Economie Politique, 1867, tome I, p. 47. 

^ Principles of Social Economy, English translation, p. 50. 

^ Theories of Production and Distribution, London, 1894, p. 14. 

' Among them are Cannan's History of Theories of Distribution, 
Hadley's Economics, Smart's Distribution of Income, Daniels's Fi- 
nance, Fetter's Principles of Economics, Seligman's Principles of Eco- 
nomics. 

8 See "What is Capital?" loc. cit. 

' In his Growth of Capital. 

^^ In his "Wealth of France and of Other Countries," English 
translation, Journal of the Royal Statistical Society, 1894. 

** Economic Principles, London (Methuen), 1904, pp. 16-18. 



Sec. 6] CAPITAL 61 

Nicholson/ Hicks/ and the "Committee [of the British 
Association for the Advancement of Science] on a Common 
Measm-e of Value in Direct Taxation," ^ Professor Mar- 
shall says that in earlier years he "invariably thought of 
capital as the whole stock of goods, and of interest as the 
whole of the usance or benefits derived from the use of that 
stock";* that "when one approaches the problem of dis- 
tribution from the mathematical point of view, there is 
practically no choice" ^ but to do so; and that "wealth in 
the form of houses or private carriages helped to give em- 
plo3niient to labour as much as when in the form of hotels 
or cabs." ® He expressly concedes what is really the chief 
contention of the present writer when he says: "I concur 
in his [my] conclusion that whatever we do with the word 
capital, we cannot solve problems of capital by classifying 
wealth," ^ Yet he concludes, "not without doubt, that it 
is best to" ^ base his definition of capital on such a classi- 
fication, purely out of deference to what he conceives to be 
the dominant usage. 

§6 

As to popular and business usage, it may be said that a 
careful study of this usage as reflected by lexicographers, 
who have sought from time to time to record it,^ reveals 
the fact that before the time of Adam Smith capital was 
not regarded as a part of the stock of wealth, but as synony- 
mous with that stock.^^ Sometimes the inclusion of all 

^ In his Elements, pp. 42, 43. 

^ Lectures on Economics, Cincinnati, 1901, pp. 91, 244. 
^ Report of British Association for Advancement of Science, 1878, 
Dubhn, p. 220. 

* "Distribution and Exchange," Economic Journal, 1898, p. 56. 
5 Ihid. p. 55. 8 Ihid. p. 57. ^ Ihid. p. 50. » Ibid. p. 56. 

* See the writer's "Precedents for Defining Capital," loc. cit., where 
are presented the results of an examination of seventy-two diction- 
aries. 

^° Originally .the term "capital" was not a noun, but an adjective. 
" Capitalis pars debiti " indicated the principal part of a debt, i.e. the 
"principal " as distinguished from the interest. This virtually repre- 



62 NATURE OF CAPITAL AND INCOME [Chap, IV 

stock as capital was explicit, as, for instance, in the year 
1611, Cotgrave defined capital as, "wealth, worth; a stocked 
Again, we find : — 

1678, Dufresne du Cange, Glossarium. — Capitale dicitur bonum 
omne quod possidetur. . . . 

More often capital is explained as a term employed in 
business, as : — 

1759, Rider, W, A New Universal English Dictionary. . . . 
London. — Capital. Among merchants, the sum of money brought 
in by each party to make up the common stock. Likewise the money 
which a merchant first brings into trade on his own account. 

Here the phrase "among merchants" is perhaps intended 
to specify the sphere in which the term is generally found, 
rather than as a necessary limitation to that sphere, just 
as "hawser" is explained as a "nautical term" without 
implying that a hawser could not be employed on shore. ^ 

With the advent of the economists the dictionary 
definitions were thrown into confusion, although the great 
majority of them continue still to adhere to the original 
usage; e.g. : — 

1883, Simmonds, P. L. The Commercial Dictionary. . . . Capital 
. . . the net worth of a party. 

1894. Palgrave's Dictionary of Political Economy, under "Assets." 
The assets remaining after the discharge of liabilities are a person's 
actual capital. 

In many cases it is thought necessary to distinguish 
between the meaning of capital among economists and its 
meaning among business men ; e.g. : — 

1893, Murray, J. A. H. A New English Dictionary. . . . Vol. II, 
Oxford. — Capital, B. sh. 3. A capital stock or fund. a. Comtnerce. 
The stock of a company, corporation, or individual with which they 
enter into business and on which profits or dividends are calculated; 

sented the distinction between a fund and a flow. The term soon 
became applied to a merchant's stock in contradistinction to the flow 
of profits springing from it, and hence to any fund or stock what- 
ever. See "Precedents for Defining Capital," Quarterly Journal of 
Economics, May, 1904, p. 395. 
^ See "Precedents," pp. 8, 9. 



Sec. 6] CAPITAL 63 

in a joint stock company, it consists of the total sum of the contribu- 
tions of the shareholders, b. Pol. Econ. The accumulated wealth of 
an individual, company, or community, used as a fund for carrying 
on fresh production; wealth in any form used to help in producing 
more wealth. 

In business manuals and articles on practical account- 
ing we find that capital is employed in the sense of the 
net value of a man's wealth. Thus L. W. Lafrentz, speak- 
ing of the difference between assets and habiUties/ states : 
"The residue will be the net worth of the proprietor — 
the capital of the proprietor." 

Inquiry among business men also reveals the fact that 
in business usage all wealth is included in the term "capital." 
It would astonish a business man to have an economist 
strike out from his assets as non-capital his raw materials, 
as would Kleinwachter ; his perishable goods, as would 
Hermann; his fuel, as would Walras; or, above all, his 
land, as would most of the classical economists. That land 
is capital, business men all emphatically declare. As the 
manufacturer would express it, land is the very first thing 
into which the "paid-in" capital of a new concern is con- 
verted. Again, business men maintain that the function 
of any given wealth has nothing to do with its classification 
as capital. It need not be "for production" nor "for sus- 
taining laborers," nor for any particular object whatever. 
The only point on which some of them hesitate is whether 
or not all articles in consumers' hands are capital. The 
reason for this hesitation may possibly be found in the cus- 
toms of bookkeeping. As one business man expressed it, 
"Capital is simply a bookkeeping term." Consequently 
the business man naturally associates the term with his 
shop and not his home, for he keeps a balance sheet in the 
former and not in the latter ; but, once given a balance sheet, 

1" Economic Aspects of Accounting and Auditing," Journal of 
Accountancy, April, 1906, p. 482. Cf . Victor Branford, Economics and 
Accountancy, London (Gee & Co.), 1901, and Charles E. Sprague, The 
Accountancy of Investment, New York (Business Publishing Co.), 1904, 
p. 12. 



64 NATURE OF CAPITAL AND INCOME [Chap. IV 

it does not matter what purpose is behind it. A social 
club, an art gallery, or a hospital may have a capital. 
In one year a joint stock company with capital stock was 
proposed for the purpose of building the yacht for defend- 
ing the America Cup. If a private family should call it- 
self a joint stock company and draw up a balance sheet, 
entering all its property, house, furniture, provisions, etc., 
on one side, with the debts on the other, no business man, 
we imagine, would hesitate to call the balance of assets over 
liabilities, which is the total wealth-value of the family, 
by the name "capital." As a business man said to 
the writer, "Capital isn't a part of wealth, but all a 
man has got, including his automobile." "Is that cigar 
in your mouth capital?" he was asked. "No," he said, 
hesitatingly; but this opinion he quickly reversed as in- 
consistent with his former statement, and admitted that a 
box of cigars and each cigar in it, or out of it, for that matter, 
were a part of his stock or reserve. 

The phrases "to capitalize" and "to Uve on capital," 
as used by business men, imply that capital is simply a fund. 
When we "capitaUze" an annuity of $5 a year at a 
given sum, as $100, we mean that $100 is the fund of 
ready-money equivalent of $5 flowing in annually. It does 
not matter what kind of goods the $5 of income or the 
$100 of capital represents. Again, when we say that a 
man is "Uving on capital," we mean that he is using up 
his stock faster than he is replacing it. The reference 
is not to any particular part or kind of the stock. A 
wealthy New Yorker who was recently forced to "live 
on capital" did so by selling his accumulations of art treas- 
ures; it would be the same if he had sold his stocks and 
bonds. 

So far, then, as popular and business usage is concerned, 
we have ample warrant for the definition of capital here 
accepted, and no warrant whatever for the definitions 
ordinarily found in economic text-books. 



Sec. 7] CAPITAL 65 

§7 
Should economists continue to reject the simple defi- 
nition above explained, and insist on restricting the 
term capital to some narrower meaning, our only re- 
course will be to follow the example of John Rae,^ and, 
after defining capital as a part of stock, quietly shelve 
the term and proceed to the analysis of "stock" instead.^ 
We shall then be in the curious position of acknowledging 
that the "problems of capital ' 'are not problems of " capital " 
only, but of stock, and shall have to regard such common 
phrases as "the interest on capital," "I'interit du capital," 
and '' capitalzins" as misnomers. But this or any other 
settlement of the difficulty will be welcome to all who are 
tired of the present confusion of tongues. A business friend 
recently complained that he was chiefly deterred from read- 
ing the books of economists because they seemed to have no 
settled terminology. It does not so greatly matter what 
name we select by which to call a concept. The important 
matter is to select for consideration those concepts which are 
fruitful in scientific analysis. That the concept — by what- 
ever name we call it — of a stock of wealth at an instant of 
time is thus fruitful will, we believe, appear more plainly 
as we proceed to apply it to what have been called, rightly 
or wrongly, the "problems of capital." 

^ Sociological Theory of Capital, edited by Professor Mixter, Mac- 
millan, 1905. 

^ It is not, of course, denied that " stock " falls into several more or 
less distinct groups. One classification has already been given in the 
chapter on "Wealth," and there are many others. One of the most 
striking divisions of the stock of wealth as it exists in modern society 
is between that at home and that in business. This is the basis of 
many definitions of capital, especially that of Komorzynski (Credit, 
Innsbruck, 1903, p. 138). But the distinction applies only to modern 
and highly differentiated societies. Like all classifications of concrete 
things, it serves a descriptive purpose but does not help analysis. 
It is well known that in science the most general conceptions are 
the most fruitful. Professor J. Willard Gibbs, noted for the gen- 
erality and simplicity of his methods in mathematical physics, used 
to say, "The whole is simpler than its parts." 

F 



CHAPTER V 

CAPITAL ACCOUNTS 
§1 

We have defined capital as a quantity of wealth existing 
at an instant of time. A full view of capital would be 
afforded by an instantaneous photograph of wealth. This 
would reveal, in addition to the durable wealth, a large 
amount of goods of rapid consumption. It would disclose, 
not the annual procession of such goods, but the members 
of that procession that had not yet been transmuted in 
form or passed off the stage of existence, however swiftly 
they might be moving across it. It would show train- 
loads of meat, eggs, and milk in transit, cargoes of fish, 
spices, and sugar, as well as the contents of private pantries, 
ice chests, and wine cellars. Even the supplies on the table 
of a man bolting his dinner would find a place. So the 
clothes in one's wardrobe or on one's back, the tobacco in 
a smoker's pouch or pipe, the oil in the can or lamp, 
would all be elements in this flash-light picture of capital. 

Such a collection of wealth is, however, heterogeneous; 
it cannot be expressed in a single sum. We can inventory 
the separate items, but we cannot add them together. 
They may, however, be reduced to a homogeneous mass by 
considering, not their kinds and quantities, but their 
values. And this value of any stock of wealth is also called 
"capital." To distinguish these two senses of capital, we 
call a stock, store, or accumulation of existing instruments 
of wealth, each instrument being measured in its own unit, 
capital-instruments, or capital-wealth, and we call the 
value of this stock, when all articles are measured in a com- 



Sec. 1] CAPITAL ACCOUNTS 67 

mon unit, capital-value. Similarly, a quantum of property 
rights existing at any instant is called capital-property, 
and its value, capital-valice. As a general term to include 
both capital-instruments and capital-property, we may 
employ capital-goods, a term first suggested by Professor 
Clark. 

We have, then, a definite antithesis between capital- 
goods and capital-value, capital-goods being measured in 
various units appropriate to the various goods, as, for in- 
stance, in bushels of wheat, gallons of oil, acres of land, 
shares of stock, and capital-value being measured in a 
single uniform manner, as in dollars or other convenient 
units of value. The simple term "capital" is only em- 
ployed as an abbreviation of either of the compound terms 
"capital-goods" and "capital- value." The business man 
ordinarily uses the term "capital" in the sense of capital- 
value, and hereafter, unless it is otherwise specified, the 
term "capital" will be understood in this sense. In 
adopting this nomenclature we find ourselves in harmony 
with Professors Clark, Fetter, Tuttle, and others referred to 
in the preceding chapter. 

We are now ready to consider the "capital accounts" 
employed in business. It is strange that any treatment 
of these accounts is generally omitted from economic 
text-books. There seems to be no systematic study of capi- 
tal accounts in any work on political economy. 

A capital account is a statement of the amount and 
value of the property of a specific owner at any instant of 
time. It consists of two colirams, — the assets and the 
liabilities. The liabilities of an owner are the debts and 
other obligations owing to others; that is, they are the 
property-rights of others for which such owner is respon- 
sible. The assets or resources of the owner are all his prop- 
erty-rights, irrespective of his liabilities. The assets 
include both the property which makes good the liabilities, 
and the property, if any, in excess of the liabilities. They 



68 NATUKE OF CAPITAL AND INCOME [Chap. V 

^^ also include, if exhaustively considered, the person of the 

owner himself. 

The owner may be either an individual human being, or 
a collection of human beings, such as a family, an asso- 
ciation, a joint stock company, a corporation, or a govern- 
ment. With respect to a debt or Hability, the person 
who owes it is the debtor and the person owed is the 
creditor. 

Every item in a capital account is an element of the 
owner's total capital, the assets being positive elements 
and the liabilities being negative. Consequently, the alge- 
braic sum of the elements of capital, or the difference in 
value between the total assets and the total liabilities, is the 
net capital, or capital-balance indicated in the account. 

§2 

The items in a capital account are constantly changing, 
and their value also, so that when, after one statement of 
assets and liabilities is drawn up, another is constructed at a 
point of time six months later, the balancing item, or net 
capital, may have changed considerably. However, book- 
keepers are accustomed to keep the item "capital" intact 
from the beginning of their account, and to denominate any 
increase of it as "surplus" or "undivided profits." There 
are several reasons for this. In the first place, the less 
often the bookkeeper's entries are altered, the simpler the 
bookkeeping. Again, by stating separately the original 
capital and its later increase, the books show at a glance 
what the history of the company has been as to the accumu- 
lations of capital. Finally, in the case of joint stock com- 
panies, the capital is represented by stock certificates, the 
engraved "face value" of which cannot conveniently be 
altered to keep pace with changes in real value. Conse- 
quently it is customary for bookkeepers to maintain the 
book value of the "capital" equal to the face value of the 
certificates. 



Sec. 2] CAPITAL ACCOUNTS 69 

The following two balance sheets will show the accu- 
mulation of "surplus." 

January 1, 1900 

Assets Liabilities 

Plant $200,000 Debts $100,000 

Capital , . . . . 100,000 

$200,000 $200,000 

January 1, 1901 

Plant, etc $246,324 Debts $100,000 

Capital 100,000 

Surplus 46,324 

$246,324 $246,324 

But not only is the book item, capital, maintained intact 
as long as possible, but often the surplus also is put in round 
numbers and kept at the same figure for several succes- 
sive reports. All the smaller fluctuations have an effect 
simply on a third item called "undivided profits." The 
distinction between surplus and undivided profits is thus 
merely one of degree. The three items — capital, surplus, 
and undivided profits — together make up the present net 
capital. Of this, "capital" represents the original amount, 
"surplus" the earHer and larger accumulations, and "un- 
divided profits " the later and minor. The undivided profits 
are more likely to appear in dividends, that is, to become 
divided profits, although this may also happen to the surplus, 
or even in certain cases to the capital itself. 

We see, then, that the capital of a company, firm, or 
person is to be understood in two senses; first, as the 
item entered by the bookkeeper under that head, — the 
original capital; and, secondly, this sum plus surplus and 
undivided profits, — the true net capital at the instant 
under consideration. 

Inasmuch as the stock certificates were issued at the 
formation of the company and cannot be perpetually 
changed, they ordinarily correspond to the original instead 



70 NATURE OF CAPITAL AND INCOME [Chap, V 

of to the present capital. Recapitalization may be ef- 
fected, however, by recalling the stock certificates or issu- 
ing new ones. In these ways the nominal or book value 
may be either decreased or increased. It is sometimes 
scaled down because of shrinking assets, and often increased 
because of new subscriptions or expanding assets. If, for 
instance, the original capital was $100,000, and the present 
capital (that is, including surplus and undivided profits) 
is $200,000, it would be possible, in order that the total 
certificates outstanding might become $200,000, and the 
surplus and undivided profits be enrolled as capital, to 
issue free to each stockholder stock certificates of a face 
value equal to those already held. In practice, how- 
ever, such a proceeding is very rare. Ordinarily the stock 
certificates remain as originally, and merely increase in 
value. Thus, if the present capital is as in the above 
example, $200,000, whereas the original capital and the 
outstanding certificates amount to only $100,000, the 
market value of the shares will be double the face value; 
for the stockholders own a total of $200,000, represented 
by certificates of the face value of $100,000. 



If, however, we attempt to verify such a relation by 
reference to the company's books, we shall find some dis- 
crepancies in the results. For instance, the Second National 
Bank of New York had, at a recent statement, a total 
capital, surplus, and undivided profits of $1,295,952.59, of 
which the original capital was only $300,000. We should 
expect, therefore, that the stock certificates, amounting 
to $300,000, would be worth $1,295,952.59, or, in other 
words, that each $100 of stock certificates would be worth 
$432. The actual selling price, however, is found to be 
$700. Again, the Fourth National Bank of New York 
City had a total capital, surplus, and undivided profits of 
$5,700,000, of which $3,000,000 was capital. From this 



Sec. 3] CAPITAL ACCOUNTS 71 

we should expect the shares to sell at l%,o,m —^^^- The 
actual selling price, however, is $240. Here are discrep- 
ancies which call for explanation. If a business man were 
called upon to explain them, he would say that book 
values and market values are entirely distinct, the latter 
depending on estimated "earning power," The stock is 
worth its "capitalized earning power," and its value 
fluctuates from day to day in response to a thousand 
causes. This is quite true, but it does not constitute a dis- 
tinction between book values and market values, for book 
values also represent estimated earning power. The book 
valuations of the company's lands, buildings, machinery, etc., 
were originally determined by their earning power; their 
cost value was, at the time of purchase, a market estimate 
of earning power as truly as the market price of stock. This 
principle holds true of liabiHties as well as of assets. The 
liabihties are simply capitalized charges, interest, rentals, 
and other expenses. 

The meaning of the discrepancy is, therefore, not that one 
valuation depends on earning power and the other not, 
but that there are two estimates, one that of the book- 
keeper, which is seldom revised and usually conservative, 
and the other that of the market, which is revised daily. 
Thus the stockholders of the Second National Bank are 
credited by their bookkeeper with owning $1,295,952.59, 
whereas in reality the total value of their property is more 
nearly $2,100,000. The bookkeeper has systematically 
undervalued the assets of the bank, and even omitted some 
valuable assets altogether, such as good will. The object 
of a conservative business man in keeping his books is not 
to give mathematical accuracy, but to make so conserva- 
tive a valuation as to be well within the market, even in 
times of financial stress. He is more interested in safety 
than in precision, and in maintaining his solvency even in 
the face of heavy shrinkage of market values than in meet- 
ing the requirements of ideal statistics. 



72 



NATUKE OF CAPITAL AND INCOME 



[Chap. V 



There are thus two valuations of the capital of a com- 
pany, — the bookkeeper's and the market's. The latter is 
apt to be the truer of the two, although it must be remem- 
bered that each of them is merely an appraisement. We 
see, therefore, that the balance of a company's books which 
is so carefully worked out to the last cent, and which has 
so imposing an appearance of accuracy, may be in reality 
very wide of the mark. 

§4 

Not only is there a discrepancy between the market esti- 
mate of the present capital of a company and the book- 
keeper's entries, but the original capital paid in to the 
company may itself have been quite different from the 
nominal capitalization, for the stock may have been sold 
below or above par. We see, then, that the "capital" of a 
person or firm has four separate meanings : — the nominal 
"capitalization"; the actual original "paid-in capital"; 
the present accumulated capital, or "capital, surplus, and 
undivided profits" as given by the bookkeeper; and the 
market estimate of the same, i.e. the "value of the shares." 
These and the other senses of capital are given in the 
following scheme, which displays the various uses of the 
term "capital." 



Capital 



' Capital-goods 



I Capital- value 



e apital-instruments 
c apital-property 

assets and liabilities 
in general 



. net capital 



original 
capital 



present 
capital 



f nominal capitali- 
j zation 
I actual paid-up 
[ capital 

as recorded in 
the company's 
books, consist- 
ing of capital, 
surplus, and un- 
divided profits 

market value of 
the shares 



Sec. 5] CAPITAL ACCOUNTS 73 

§ 5 

We have seen that the effect upon the balance sheet of 
an increase in the value of the assets was to swell the sur- 
plus or the undivided profits. Reversely, a shrinkage of 
value tends to diminish those items. For instance, if the 
plant of a company having a capital of $100,000 and a 
surplus of $50,000 depreciates to the extent of $40,000, the 
effect on the books will be as follows : — 







Original Balance Sheet 






Assets 






Liabilities 


Plant . , , 
Miscellaneous 


• • 


$200,000.00 
101,256.42 


Debts 
Capital 
Surplus 
Undivided 


profits 


$150,000.00 

100,000.00 

50,000.00 

1,256.42 




$301,256.42 


$301,256.42 






Present Balance Sheet 






Assets 






Liabilities 




Plant . . 
Miscellaneous 




$160,000.00 
101,256.42 


Debts 
Capital 
Surplus . 
Undivided 


profits 


$150,000.00 

100,000.00 

10,000.00 

1,256.42 




$261,256.42 


$261,256.42 



Here the shrinkage in the value of the plant, as recorded 
on the assets side, comes out of the surplus as recorded on 
the liabilities side. 

In case the surplus and undivided profits have both 
been wiped out, the capital itself becomes impaired. In 
this case the bookkeeper may indicate the result by scaling 
down the capitalization. This sometimes occurs in banks 
and trust companies, but not often in ordinary business. It 
is often avoided by making up the deficiencies through 
assessment of stockholders or postponement of dividends. 
This is required by law in many cases, as in that of insurance 
companies. Dishonest concerns, however, often conceal the 
true state of the case by the reverse process of exaggerating 



74 NATURE OF CAPITAL AND INCOME [Chap, V 

the value of the assets. Sometimes this is done systemat- 
ically, as in the case of stock-jobbing concerns. Unscrupu- 
lous promoters often invest the sums entrusted to them 
by confiding stockholders, in unwise or fraudulent ways. 
For instance, we may imagine an Oil Well Company in 
California, of the type called "stock-producing wells," 
which borrows $50,000 and collects $50,000 more from the 
sale of stock (at par), and with this $100,000 purchases 
land of friends at a fancy price, collusively providing that 
the proceeds be returned in large part to the promoter. 
In such a case the books of the bubble concern will show 
the following figures : — ^ 

Assets Liabilities 

Land $100,000 Debts $50,000 

Capital 50,000 



$100,000 $100,000 

But if the land is worth, say, only $60,000, these accounts 
should read : — 

Assets Liabilities 

Land $60,000 Debts $50,000 

Capital 10,000 



$60,000 $60,000 

In other words, the investor has only $10,000 worth of 
property, instead of the $50,000 which he put in, or 20 
cents for every dollar he invested. The rest has been 
diverted into the pockets of the promoter and those in 
collusion with him, 

A favorite method of concealing the real condition of a 
company is to enter among the assets the bad debts due it, 
at their nominal value. Sometimes bad debts are bought 
up for that special purpose, the fraudulent company invest- 
ing in the notes of some bankrupt concern, which can be 
obtained for very little, but may be entered on the books 
at face value. It is clear that any exaggeration on the 
assets side of the ledger produces an equal exaggeration of 



Sec. 6] CAPITAL ACCOUNTS 75 

the capital, surplus, and undivided profits, on the opposite 
side. A great responsibility, therefore, rests on those who 
construct commercial accounts. 

§6 

Thus far we have considered the fluctuations of the 
items of a capital account independently of any payments 
between the company and the stockholders. When pay- 
ments are made to the stockholders in the shape of divi- 
dends, the effect is to reduce both sides of the account, de- 
pleting the cash on the assets side, and the undivided profits 
on the liabilities side, each by the amount of the dividend. 
If a dividend is declared larger than the undivided profits, 
the effect will be to reduce the surplus, or even the capital. 
For most business concerns it is regarded as bad policy, 
or even fraudulent, to pay dividends out of capital. How- 
ever, there is no inherent reason why such dividends 
should not be paid, and in some sorts of business it is not 
only proper but necessary. In these cases when divi- 
dends are paid out of capital there should be a corre- 
sponding reduction in the amount of outstanding capital 
stock, in order that those dealing with the concern may not 
be deceived. For instance, land companies in Colorado 
and California, such as the Redondo Land Company, are 
formed for the express purpose of investing in land and sell- 
ing it again. As fast as it is sold, the proceeds are divided 
among the stockholders, and stock certificates cancelled, 
until the whole capital of the company is cleared away. 
Ordinarily, however, reduction in capital takes other forms 
than dividend payments. The payment of dividends out 
of capital is, generally speaking, unlawful, otherwise the 
creditors of a company might suddenly find themselves 
without any adequate security for their loans. 

Payments are, of course, also made from the stock- 
holders to the company. We will suppose that a company 
is formed with a capital stock of $100,000, but that when its 



76 NATUKE OF CAPITAL AND INCOME [Chap. V 

first statement is made only $60,000 of this stock has been 
subscribed. It would be possible for the bookkeeper to 
enter the capital at that moment as $60,000; but, follow- 
ing his rule of keeping the capital item the same in all suc- 
cessive accounts, he will place the whole $100,000 on the 
liabilities side, and, to offset it, will insert on the other side 
assets of $40,000 in the form of treasury stock, the idea 
being that the company holds, in its treasury, stock cer- 
tificates for $40,000, which are to be regarded as an asset. 
Of course this mode of entering treasury stock is a book- 
keeping fiction, for this sum of $40,000 represents what 
is neither owned by nor owing to the company, except in the 
sense that the company owes itself; yet promoters will 
often impose upon the credulous investor the statement that 
to keep a certain amount of the stock of the company in its 
own treasury increases by that much the property of the 
stockholders. 

After the capital stock has been fully paid in, it is often 
necessary to enlarge it. Let us suppose that before the 
increase in capital the account stands as follows : — 

Assets Liabilities 

Miscellaneous . . . $300,000 Debts $100,000 

Capital 100,000 

Surplus and undivided 

profits .... 100,000 

$300,000 $300,000 

Next let new capital to the extent of $100,000 be issued 

and sold to old stockholders at par, in lots proportionate 

to their original holdings. The new stock certificates of 

face value of $100,000 are thus sold for $100,000. The 

accounts will then stand as follows : — 

Assets Liabilities 

Miscellaneous . . . $400,000 Debts $100,000 

Capital 200,000 

Surplus and undivided 

profits .... 100.000 

$400,000 $400,000 



Sec. 7] CAPITAL ACCOUNTS 77 

The additional capital will first take the form of cash, 
but afterward, by the purchase of plant, equipment, etc., 
wiU be changed into these or other forms of wealth or 
property. We shall suppose, however, for the present, that 
in whatever form invested, the value remains exactly equal 
to the cost, namely, $100,000, so that the assets are 
changed from $300,000 to $400,000. 

§ 7 ■ 

Let us assume that the books accurately represent actual 
values and correspond to market prices. After the new issue 
of stock, we find $200,000 of stock certificates representing 
$300,000 of actual value of capital, surplus and undivided 
profits, or $150 per share. But the new stock was, we 
assumed, issued to them at $100 a share. Hence the 
original stockholders will be able to make a profit on their 
new stock by buying at the issue price of $100 and then 
selling at $150 ; or they may shorten this operation by sell- 
ing their "right to subscribe" for $50. At first sight it 
would seem as though this right to subscribe represented 
a mysterious bonus to the stockholders, due to the issue of 
the new stock. It must be remembered, however, that 
the $100,000 par value of original stock certificates repre- 
sented, including the surplus, $200,000 worth of property 
belonging to the stockholders, consequently the original 
certificates were worth $200 per share. That is, the efi'ect 
of issuing new stock below the original market price was 
to lower the value of the old stock from $200 per share to 
$150 per share. Consequently the loss of $50 to the stock- 
holders on their old stock will exactly compensate for the 
$50 of excess value represented in the rights to subscribe. 
An individual stockholder owning 10 of the original shares 
will find them worth, instead of $2000, only $1500, that is, 
he will lose $500. This will equal the profit of $500 on 
his 10 new shares or the value of his rights to subscribe 
for them. The outside public would be willing to pay 



78 NATURE OF CAPITAL AND INCOME [Chap. V 

him $500 for the privilege of buying $1500 worth of stock 
for $1000. 

We thus see that the price at which the new stock is 
issued does not of itself affect the balance due the share- 
holders. And yet the price of issue is not a matter 
of indifference. The lower the price of issue, the greater 
the inducement to the individual stockholder to subscribe, 
or to find some one else to subscribe instead, and buy his 
"right." Neglect to subscribe (or to sell the right to sub- 
scribe) would then cause a loss. The value of the old shares 
will be lowered in any event, and in such subscription or 
sale lies the only means of indemnification. For these 
reasons, it is usual for new stock to be offered to the original 
stockholders below the market price. 

The exact compensation between the value of the new 
rights and the depreciation of the old stock is seldom realized 
in practice, because the company may be in a position to 
invest the new sums to advantage, in other words, to buy 
assets which are worth more than cost. In this case there 
may be Uttle or no loss in the value of the old shares. But 
the point emphasized still remains true, that the price 
of issue does not of itself create additional capital value 
through the "right to subscribe." Any increase of value 
will be due to unusual opportunities for investment, — to 
economic causes and not to mere bookkeeping changes. 

Of course, it may be true that the very fact of issu- 
ing new shares may of itself create a different opinion 
in the stock market and influence prices there for better or 
worse. A low price of issue may, for instance, make the 
stock more available for small investors, and the conse- 
quent increase in the volume of the stock on the market 
may make it, temporarily at least, a subject for the specu- 
lation of pools. Such facts, while they modify the results, 
do not affect the principle. 



Sec. 8] CAPITAL ACCOUNTS 79 

§8 

We have considered two ways through which the book- 
value of capital, surplus, and divided profits may ex- 
aggerate the true condition of the stockholders' property, 
namely, through misfortune or the unforeseen shrink- 
age of the assets, and through misappropriation of stock- 
holders' funds, even when stock had at the outset been 
issued at par. There remains to be considered a third 
way, namely, through the issue of stock below par, or for 
services, patents, etc., at unduly high prices. 

To illustrate this way of overvaluing capital, or " stock- 
watering," suppose a company to be capitahzed at $200,000, 
and that this company issues at the beginning 1000 certifi- 
cates of the par value of $100,000, but sells them for only $60 
per share actually paid into the treasury. Here is $60,000 
paid-in capital, represented by $100,000 face value of stock 
certificates, leaving a margin of $40,000 " water." Sup- 
pose, further, that another block of $100,000 of the stock is 
given to an inventor for his patent, the real value of which 
is only $10,000. Finally, suppose that bonds are issued 
to the extent of $300,000, and are floated at par. Then the 
company has received in actual cash only $360,000. Of 
this sum only $60,000 has been received from the stock- 
holders. The patent, which has also been contributed in 
return for $100,000 of stock, and which is worth only one 
tenth of that sum, makes the total balance due the stock- 
holders $70,000. But, the company is capitahzed at 
$200,000. Consequently it will be necessary for the book- 
keeper to exaggerate the assets to the extent of $130,000. 

He may do this as follows: — 

Assets Liabilities 

Plant [cost S360,000] . $400,000 Bonds $300,000 

Patent [worth 10,000] . 100,000 Capital 200,000 

$500,000 $500,000 

Here $90,000 of the exaggeration is put under patent 
and the remainder in an overvaluation of the plant. Many 



80 NATURE OF CAPITAL AND INCOME [Chap. V 

other methods of stock-watering are possible. A common 
one is to allow the plant to run down; i.e. to fail to make 
proper repairs, while retaining its old book value in the 
balance sheet. A railway may be "skinned" in this way, 
by diverting to dividends what should be paid to a depre- 
ciation account. This operation, however, is not com- 
monly called stock-watering, but mismanagement. 

It is sometimes said that stock-watering is not wrong, 
as long as all the terms and conditions are known. This 
is much Hke saying that lying is not wrong, provided every- 
body knows that it is lying; for a false balance sheet 
is only one form of a false statement, and, ordinarily, a 
false statement is made with intent to deceive. The object 
may be, for instance, to mislead intending bondholders by 
making them believe that there is a larger security for their 
loans than actually exists. We see here one reason why 
honest men often undervalue their assets. They prefer, 
if there is any error in their valuations, that the error 
shall be against themselves rather than in their favor; 
in other words, that their representations as to finan- 
cial strength shall be well within the truth. Yet it 
not infrequently happens that undervaluations of assets 
may, like overvaluations, serve the purposes of dishonesty, 
— to "bear" the speculative market, for instance. 

Many attempts have been made to prevent the frauds 
which result from stock-watering. For instance, the State 
or National governments compel publicity of accounts in 
the case of insurance companies, national banks, and inter- 
state railways. The stock exchanges require similar pub- 
Hcity in regard to "listed" securities. Any company whose 
securities are listed on the New York Stock Exchange 
must pubUsh its assets and habilities at stated intervals. 
But this rule is too general to be very effective. In some 
cases the law requires the entire nominal capital to be paid 
into the company, in cash or securities at their market 
value, as in the case of national banks. ^ 

1 Revised Statutes, § 5140 (Act June 3, 1864, § 13). 



Sec. 9] CAPITAL ACCOUNTS 81 

§ 9 

The original capital of a concern may therefore be either 
increased or decreased. In the course of its fluctuations 
it may sometimes shrink to zero. If it sinks below zero we 
have insolvency, — the condition in which assets fall short 
of liabilities. The capital-balance is intended to prevent 
this very calamity; that is, it is for the express purpose 
of guaranteeing the value of the other liabilities. 

These other Uabilities represent, for the most part, fixed 
blocks of property carved out, as it were, of the assets, and 
which the merchant or company has agreed to keep intact 
at all hazards. The fortunes of business will naturally cause 
the whole volume of assets to vary in value, but all this 
" slack" ought properly to be taken up or given out by the 
capital, surplus, and undivided profits. Capital thus acts as a 
buffer to keep the liabilities from overtaking the assets. It is 
the "margin" put up by those most interested in an enter- 
prise, as a guarantee to others who advance their capital to it. 
The amount of capital-balance necessary to make a business 
reasonably safe will differ with circumstances. A capital- 
balance equal to five per cent of the habihties may, in one 
kind of business, such as mortgage companies, be perfectly 
adequate, whereas fifty per cent may be required in another 
kind. Much depends on how likely the assets are to shrink 
and how much ; and much, likewise, on the character of the 
habihties. If the assets have stability of value, less capital 
will be required than if they consist of speculative securities. 

The risk of insolvency is, then, the chance that the assets 
may shrink below the liabilities. This risk is the greater, 
the more shrinkable the assets, and the less the margin of 
capital-value between assets and Habihties. The subject 
lends itself to mathematical and statistical treatment; 
but to work out the quantitative relations would lead us 
far afield ; it would require much statistical material, and 
its analysis by the mathematics of chances. 



82 NATURE OF CAPITAL AND INCOME [Chap. V 

§ 10 

Insolvency may exist for a time without being known; 
there may be no legal bankruptcy. Legal bankruptcy 
exists as soon as there is a legal declaration of inability 
to meet obligations. This may not be true insolvency. 
For instance, the assets may exceed the liabilities, but the 
cash assets at the particular time may be less than the cash 
liabilities due at that time. This condition we may call 
pseudo-insolvency. In such a case, a little forbearance on 
the part of creditors may be all that is necessary to prevent 
financial shipwreck. 

A wise merchant, however, will not only avoid insolvency, 
but also pseudo-insolvency; that is, he will not only keep 
his assets in excess of his liabilities by a safe margin, but 
will also see that his assets are invested in the right form 
so as to enable him to cancel each claim at the time and 
in the manner agreed upon. 

From this point of view there are three chief forms of 
assets, — cash assets, quick assets, and slow assets. A cash 
asset is property in actual money, or what is acceptable in 
place of money. A quick asset is one which may be ex- 
changed for cash in a relatively short time, as, for instance, 
call loans, short-time loans, and other marketable securities. 
A slow asset is one which can be exchanged for cash only in a 
relatively long time, as real estate, office fixtures, and manu- 
facturers' equipment. The skill of a good business man 
consists in properly marshaling these various constituents 
of his assets. 

§ 11 

When we speak of the assets falHng short of the liabilities, 
we refer only to those assets which are included in the 
balance sheet. There may be, outside of the company, 
private means of stockholders adequate to meet the debts 
of a company, but unavailable. In fact, in the case of a 
joint stock company, there is express provision for ''limited 



Sec. 11] CAPITAL ACCOUNTS 83 

liability," so that the only assets which can be considered 
in determining solvency are those on the balance sheet of 
the company. However, in some cases, as in the case of 
national banks, the stockholders are liable for double the 
amount of the capital. In the case of a partnership, on 
the other hand, the partners are liable for almost all of 
their private property, so that the individual member of 
the firm has always to reckon w^th a contingent liabiUty 
to the creditors of the firm. 

Originally, before business was separated from private 
life, all of a debtor's assets, even including his own person, 
were regarded as pledged to the payment of a debt. The 
attitude of the law and public opinion toward this matter 
has changed greatly. Only a few generations ago an in- 
solvent debtor was imprisoned, the theory being that insol- 
vency was a crime. When intentional, or due to gross 
negligence, it is; but when due to the ordinary chances of 
business it is not. To put a debtor in prison did not of 
course help him to pay his debts. When this practical point 
was admitted, special bankruptcy acts were passed to re- 
lieve insolvency if very widespread, as after a panic. Such 
acts were at first merely temporary, and regarded as 
justified only under extraordinary circumstances. To-day, 
however, laws exist by which a bankrupt may be discharged 
free of further liability, and without the necessity of any 
special legislation. The Ray Act in the United States, under 
which our present system of bankruptcy has been worked 
out, was passed as late as 1898. In some places, as in 
France, the older view of limited liabiHty still prevails; 
but the EngHsh and American system is not only sounder 
in practice, as shown by its results in encouraging legitimate 
enterprise, but is also based on sounder theory, for it 
recognizes the fact that the creditor is a risk-taker. This 
has always been and is necessarily the case, however much 
the debtor may try to safeguard his creditors' interests. 
The capital of a company exists, as we have seen, for the 



84 NATUEE OF CAPITAL AND INCOME [Chap. "V 

purpose of mimmizing this risk, but it cannot eliminate it 
altogether. 

§ 12 

The principle that a creditor of a concern is a risk-taker 
has two important corollaries. The first is that, when 
bankruptcy occurs, though the nominal liabiUties exceed 
the assets, their actual value does not. We may say that 
so far as their actual value is concerned, the value of the 
liabilities of a company can never be greater than the 
assets, for they derive their value from these assets. A com- 
pany which can pay only fifty cents on the dollar must have 
its obligations classified as "bad debts," worth only half 
their nominal amount. This fact does not, of course, 
justify the intentional repudiation of debts. Some states 
of the United States have, it is true, attempted to reduce 
the burden of their debt by offering to buy up their 
own bonds at their market price, when this price was 
below par, owing to a lack of confidence in their ultimate 
redemption. Such an operation is evidently a species of 
repudiation. 

On the other hand, we must not regard it as an unfor- 
givable sin for the bona fide bankrupt not to pay his debts 
in full. So long as the creditor understands in advance 
the nature of the risk he is taking, he must abide by the 
result. Nowadays, in the case .of investments in large 
corporations, this is perfectly well understood. Many 
railroads have been bonded for almost their entire cost, the 
bondholder reaUzing fully that he could obtain nothing 
unless the road was a success. This participation in risk 
is particularly evident in the case of income bonds, which 
specifically pay interest only so long as the road's income 
is adequate. 

The principle that the true value of the liabiUties is derived 
from the assets and can never exceed them may seem to 
have an exception in the case of a person who succeeds 
in borrowing money "without capital." It is clear, how- 



Sec. 12] CAPITAL ACCOUNTS 85 

ever, that if we employ the term "wealth" in its larger 
sense, a person who is really good for his debt is him- 
self assets to that extent. His present value must in the 
estimation' of his creditors be at least equal to the dis- 
counted value of his debt-paying power; otherwise he 
could not borrow. It follows that his liability, being only 
part of the discounted value of his debt-paying power, 
cannot exceed his assets. 

The second corollary, from the principle that all seciu-ities 
imply risk, is that the distinction between stockholders 
and bondholders is chiefly one of degree, and may be 
bridged over by intermediate forms. Preferred stock 
and income bonds amount to very nearly the same thing. 
The preferred stockholder is elevated above the common 
stockholder, and resembles a bondholder in that he is as- 
signed a certain fixed amount of the earnings before any 
accrue to the common stockholder. The income bondholder, 
on the other hand, is depressed below the other bondholders, 
and resembles a stockholder in that he will not be paid until 
the ordinary bondholders have been satisfied. The chief 
remaining differences between these two forms of security 
are that the stock confers voting power, while the bond 
does not ; and that the bond has a due date for final ex- 
tinguishment, while the stock continues until the company 
is "wound up." 

The distinction between the different classes of creditors 
of a concern is still further swept away in some cases where 
there is no capital stock, as in that of a mutual insurance 
company. Here the policy holders, instead of being 
creditors for fixed sums due them from the company, as 
are the bondholders of a joint stock concern, themselves 
assume the risk of the business and also take whatever 
chance there may be of profit. They are, as it were, both 
stockholders and creditors. In the accounts of a mutual 
company there will be almost no outside creditors. In 
such companies, therefore, bankruptcy would seem to 



86 NATUEE OF CAPITAL AND INCOME [Chap. V 

be impossible; but as their debts for death claims are 
for specific sums, they may be forced into Hquidation, if 
unable to obtain these sums by remitting dividends or by 

assessments. 

§13 

When bankruptcy occurs, the claims of creditors are 
settled in one of three ways: through an agreement of 
"composition," by which the creditor agrees to take 
what he can get and excuse the debtor for the differ- 
ence; through an assignment by the debtor of his assets 
to his creditors; or through foreclosure by the holder of 
some obligation. 

The final result of bankruptcy will be either liquidation, 
by which the business assets are sold and distributed and 
the business wound up ; or reorganization, by which the 
business is continued and the habilities are entirely changed 
in character. In the case of companies with large fixed 
capital, as, for instance, raihoads, reorganization is the 
usual result, and the old bondholders often become the 
stockholders, the old stockholders surrendering their rights 
altogether. While this reorganization is being effected, 
the affairs of the company are administered by a receiver 
appointed by the bankruptcy court. He calls in all the 
stock and bonds, and issues temporary receiver's certifi- 
cates. These in turn are exchanged for the new securities 
when ready. However, the bondholder seldom wishes to 
assume his right of control and become a stockholder, and 
is usually offered instead the option of cash or some new 
security similar in kind to that which he held before, but 
less in amount. He is apt to accept one of these alterna- 
tives, realizing that to foreclose and take possession is 
likely to be more troublesome, and, in the end, less advan- 
tageous. Thus the losses of the old company are "written 
off," and the reorganized company starts afresh with a clean 
set of books. The change is simply a change in the forms 
of ownership of wealth and in the individual owners. 



Sec. 14] 



CAPITAL ACCOUNTS 



87 



§14 

The bankruptcy of one firm often causes the bank- 
ruptcy of another. The interdependence between firms 
may be clearly seen in the following table, where the liabil- 
ity of one person is represented by the asset of another, 
thus : — 

Person A 



Assets 
Miscellaneous . . , 


Liabilities 

. $100,000 Note to B .... 

Capital 


$50,000 
50,000 




$100,000 


$100,000 




Person B 




Assets 
A's note .... 
Miscellaneous . . . 


Liabilities 
. $50,000 Note to C et al. . . . 
. 20,000 Capital 


, $40,000 
, 30,000 




$70,000 


$70,000 




Person C 




Assets 
Note of B . . . . 
Miscellaneous . . . 


Liabilities 
. $20,000 Bills to Detal. . . . 
. 20,000 Capital 


, $10,000 
, 30,000 




$40,000 

Person D 


$40,000 


Assets 
Due from C . . . . 
Miscellaneous . . . 


Liabilities 
. $5000 Miscellaneous . . . 
. . 4000 


. $9000 



$9000 



$9000 



Now suppose A fails, for the reason that his assets un- 
expectedly shrink to $10,000, that is, become $90,000 less 
than they were before. Then the value of the liabilities 
shrinks $90,000. This wipes out all of A's capital of $50,000, 
and takes $40,000 from the value of the rest of his liability, 
which was a note to B. B gets, therefore, only $10,000 
out of a claim of $50,000 or only 20 cents on the dollar. 
In B's account this note of $50,000 must now be scaled 



88 NATURE OF CAPITAL AND INCOME [Chap. V 

down as a bad asset worth only $10,000 instead of 
$50,000 ; that is, B's assets shrink $40,000. A's loss is thus 
enough to wipe out all of B's capital of $30,000, and pare 
down the value of his other liabilities by $10,000, so that B 
can now pay only $30,000 out of the $40,000 he owes. In 
other words, he is able to pay only 75 cents on the dollar. 
Next comes C, who has $20,000 invested in B's note. He 
gets only 75 cents on the dollar, so that this asset, nominally 
worth $20,000, is found to be worth only $15,000, and his 
loss is only $5000. This loss is not enough to wipe out all 
his capital, but only reduces it from $30,000 to $25,000, 
so that C remains solvent. Consequently D, who owns C's 
bills for $5000, will lose nothing. The force of the catas- 
trophe has been spent. It ruined A and B and injured C, 
but stopped short of D. 

From this example we may see that the statistics of 
bankruptcies are often misleading. Thus, it is usual for 
the statistician to sum up the liabilities of all bankrupt 
firms. But in case the various firms are connected, as in 
the above example, the total sum lost is not as great as 
though the same amount of bankruptcy occurred in inde- 
pendent firms. In the preceding example the only loss is 
$90,000, all in A's assets. But there would appear to be 
a loss of $90,000 in A's account, one of $40,000 in B's 
account, and one of $5000 in C's, or $135,000 in all. 
This misleading result is evidently due to counting parts 
of the loss twice and three times. 

Failures are sometimes due to a false fear of calamity, 
a shock to business confidence. This will cause a shrinkage 
of values in several ways. For instance, it will induce 
creditors to demand payment and refuse renewals of bills. 
Forced liquidation and contraction of credit are the result. 
No physical capital is destroyed, but the form of ownership 
is violently disturbed, and often the management, being 
transferred from stockholders to bondholders, is turned 
from competent to incompetent hands. Above all, the 



Sec. 15] CAPITAL ACCOUNTS 89 

expectations of the future are changed and confused. 
Plans are given up, orders are countermanded, and trade 
is stopped. Assets, representing as they do the value of 
future expectations, suffer sudden and heavy reductions. 

§15 

Briefly summarizing this chapter we may say that a per- 
son who has liabilities is, in a sense, a trustee. He holds 
more than he owns. He holds all his assets; he owns 
only the margin between these and his liabilities. His 
responsibility for the liabilities requires that he should 
keep his own margin of capital comparatively safe. But 
there is always risk of losing his margin and becoming 
insolvent. This risk, whether large or small, is necessarily 
assumed by his creditors, and its existence should be 
recognized in law as well as in business practice. The 
record of the relations which at any time exist between 
assets, liabilities, and the margin of capital separating 
them constitutes what we have called the "capital ac- 
counts." 



CHAPTER VI 

CAPITAL SUMMATION 



The interdependence of the balance sheets of different 
firms or companies which has been revealed by the com- 
munication of bankruptcies exists, of course, irrespec- 
tive of bankruptcies. It exists wherever any item 
enters two accounts, in one as asset and in the other as 
liability. In fact, every liability item in a balance sheet 
impUes the existence of an equal asset in some other bal- 
ance sheet, for every debtor impUes a creditor. Conse- 
quently every negative term in one balance sheet is offset 
by a corresponding positive term in some other. The con- 
verse, however, does not follow, namely, that every asset 
implies a liability. 

When we attempt to sima up the items in the bal- 
ance sheets of various persons, the positive and negative 
elements may be canceled out by pairs or couples. 
This method of cancellation may be called the method of 
couples. Each debt or Habihty between any two persons 
whose accounts are included, being a liability to one and 
an asset to the other, constitutes a couple or pair of equal 
and opposite items. We have already noted another way 
in which liabihties may be canceled against assets, namely, 
by subtracting the Habilities in any capital account from 
the assets in the same account. This method may be 
called the method of balances, since for each individual 
account liabilities are deducted from assets and the net 
balance is taken. Both methods must, of course, lead to 

the same result. 

90 



Sec. 1] 



CAPITAL SUMMATION 



91 



The two methods may be illustrated by the balance 
sheets of three persons, say X, Y, and Z : — 





Person X 




Assets 


Liabilities 




Z's note 

Residence . . . . 
R.R. shares . . . 


$ 30,000A Mortgage held by Y 
70,000 (Capital balance . . . 
20,000 


$50,000& 
70,000) 




$ 120,000 


$ 120,000 




Person Y 




Assets 


Liabilities 




X's mortgage . . 
Personal effects 
R.R. shares . . . 


. $50,0005 Debt to Z 

20,000 (Capital balance . . 
10,000 


$ 40,000c 
40,000) 




$80,000 


$80,000 




Person Z 




Assets 


Liabilities 




Y'sdebt .... 
Farm ..... 
R.R. bonds . . . 


S40,000C Debt to X 

50,000 (Capital balance . . , 
20,000 


$30,000« 
80,000) 



$110,000 



$110,000 



The items which appear twice, once as a liabiHty of one 
man and again as an asset of another, are indicated by the 
same letter. Thus, "A" in X's assets is matched by the 
equal and opposite item "a" in Z's liabilities. The method 
of couples thus consists simply in omitting these pairs of 
items and entering those which remain. These, in the pres- 
ent case, are all assets. 

The results of summing up the capital accounts by the 
two methods are shown in the following tables: — 



Method of Balances 


Method of Couples 


X's capital .... $70,000 


Residence .... $70,000 


Y's capital .... 40,000 


Personal effects . . . 20,000 


Z's capital .... 80,000 


Farm 50,000 




R.R. shares .... 30,000 




R.R. bonds .... 20,000 



$190,000 



$190,000 



92 NATURE OF CAPITAL AND INCOME [Chap. VI 

The totals are the same by both methods, but the method 
of balances shows the share of this total capital which is 
owned by each individual, while the method of couples shows 
the various items of capital-goods of which this total is com- 
posed, namely, residence, personal effects, farm and railroad 
shares and bonds. 

§2 

It is well to note here the distinction between the ac- 
counting of real persons and of fictitious persons. For 
a real person, the assets may be and usually are in excess 
of the Habihties, and the difference is the capital-balance 
of that person. This capital is not to be regarded as a 
liability, but as a balance or difference between the Ha- 
bihties and the assets. For a fictitious person, on the 
other hand, as for instance a corporation or partnership, 
the liabilities are always exactly equal to the assets; 
for the balancing item called capital is as truly an 
obligation from the fictitious person to the real stock- 
holders, as any of the other Kabilities. A fictitious 
person, in fact, is a mere bookkeeping dummy, hold- 
ing certain assets and owing all of them out again to 
real persons. Bookkeepers, it is true, apply the same 
methods in both cases, but they do so by regarding the 
accounts even of a real person as relating to a fictitious 
entity for bookkeeping purposes. One's business self and 
one's real self are separated. Thus if X's business shows a 
balance in X's favor of $10,000, he enters this as a 
habihty item in his business accounts and considers his 
"business" as owing him this sum. There is no objection 
to such a procedure. But we must remember that when 
we say that "X's business" owes X $10,000, we imply that 
the real X in his own accounts holds a claim of that 
amount against his "business." In other words, we are 
compelled, in order to be consistent, to open a separate 
account for X and carry forward the $10,000 balance 
to the opposite side, thus : — 



Sec. 3] CAPITAL SUMMATION 93 



X's Business 
Assets 
Miscellaneous . . . $50,000 Due to ott 

Due to X 


Liabilities 
lers . . . 


$40,000 
10,000 


$50,000 

X's Self 
Assets 
Due from "X's business " . . $10,000 


$50,000 



In the second account there is no counterbalancing 
Uability. For real persons, then, assets and habiUties are 
not equal. If they were, the summation of their balance 
sheets would yield simply zero! If we would avoid this 
absurdity, we must either omit the capital-balance from 
the liabilities side, or if for the moment we place it there, 
we must, as in the above example, carry it forward to the 
opposite side of another account, which amounts to the 
same thing in the end. 

§3 

With this preliminary explanation, let us now introduce 
into our summation the capital accounts of the railroad 
whose stocks and bonds are included among the assets of 
persons X, Y, and Z. For simplicity, we shall suppose that 
these three persons are the only persons interested in the 
road. The balance sheet of the railroad company will 
accordingly appear as follows : — 

Railroad Co. 
Assets Liabilities 

Railway ..... $50,000 Bonds (held by Z) . . $20,000 

Capital stock 

(held by X) $20,000 

(held by Y) 10,000 30,000 



$50,000 $50,000 

Now if we combine this sheet with the preceding we 
shall see that its inclusion does not affect the results 



94 NATURE OF CAPITAL AND INCOME [Chap. VI 

which were obtained by the method of balances before 
the railroad was introduced into the discussion. The 
totals will stand as follows : — 

X's capital balance $ 70,000 

Y's capital balance 40,000 

Z's capital balance 80,000 

R.R. Co.'s capital balance 000 

$190,000 

When we apply the method of couples, however, we 
find that the inclusion of the railway company's capi- 
tal account will affect the items in the final sum. The 
stocks and bonds, as assets of X, Y, and Z, will now pair off 
with the corresponding liabilities of the railroad company 
and their place will be taken by the concrete railroad itself, 
as follows : — 

Method op Couples 

Residence $ 70,000 

Personal Effects 20,000 

Farm 50,000 

Railway 50,000 

$190,000 

The appearance of the capital inventory is thus changed. 
Formerly, the items of property-rights in it included part 
rights, as stocks and bonds; now they consist only of 
complete property-rights The items still consist, strictly 
speaking, solely of property rights — the right to the 
residence, the right to the farm, etc. But, since the 
complete right to any article of wealth is best expressed 
in terms of the article of wealth itself, instead of the long 
phrase, the "right to a residence," we merely use 
"residence." The property no longer veils the wealth 
beneath it, and the inventory, which before was called 
an inventory of property-capital, is now also an inventory 
of wealth-capital. 



Sec. 3] CAPITAL SUMMATION 95 

Such a result is sure to follow when we combine capital 
accounts, provided we combine enough of them to supply, 
for every liability item, its counterpart asset, and for 
every asset which has one, its counterpart liability. The 
assets which have no counterparts are what we have 
called complete rights to wealth, or "fee simples"; those 
which have them are the partial rights to wealth. The 
reason is that every article of concrete wealth is to be re- 
garded as owned in "fee simple" by some one, even if we 
have to set up a fictitious person as dummy for that very 
purpose. Hence every part right to that wealth will nec- 
essarily appear as a liability on the opposite side of that per- 
son's account, and again as an asset on the account of some 
other person. Thus, if two brothers own a farm in 
equal shares, the farm as a whole is regarded as owned 
by the partnership person called "Smith Brothers." The 
balance sheet of this fictitious person will show as assets 
the farm and as Habihties the "undivided half-interest" of 
each brother, and these same items enter the individual 
accounts of the brothers as assets. 

To follow out capital summations thus requires the in- 
clusion of many fictitious persons, for it is often only the 
fictitious persons who hold the complete rights to articles 
of wealth. Locomotives and railway stations, for instance, 
are owned by corporations, not individuals. In fact, these 
fictitious persons — partnerships, corporations, trusts, 
municipalities, associations, and the like — are formed 
for the express purpose of holding large aggregations of 
concrete wealth and parceling out its ownership among a 
larger number of real persons. 

If, then, we suppose balance sheets so constructed as to 
include the whole world of real and fictitious persons, 
with entries in them for every asset and liability, even 
pubhc parks and streets, household furniture, persons 
themselves, and other possessions not ordinarily accounted 
for in practice, it is evident that we shall obtain, by the 



96 NATURE OF CAPITAL AND INCOME [Chap. VI 

method of balances, a complete account of the distribution 
of capital-value among real persons; and, by the method 
of couples, a complete list of the articles of actual wealth 
thus owned. On this hst there will be no stocks, bonds, 
mortgages, notes, or other part rights, but only land, 
buildings and other land improvements, commodities and 
real persons. In other words, we arrive again at the 
proposition of Chapter III, that wealth underhes and cor- 
responds to property. 

§4 

Among other part-rights in real wealth we find what is 
called "credit." There has been much discussion as to the 
nature of credit; whether, in particular, credit is to be 
regarded as a "part of capital." It has been claimed that, 
from the merchant's point of view, credit is capital be- 
cause it enables a business man to enlarge his business. 
In this view it is capital, though it is borrowed capital. 
MacLeod specifically includes credit under capital. Pro- 
fessor J. Shield Nicholson says that credit is a sort of 
revenue capital,^ but that "strictly and taking only 
material (productive) capital, this would involve counting 
the same elements twice over." We see, from our study 
of capital accounts, how to avoid such double counting. 
That part of a man's so-called capital which is borrowed 
should not enter his books as his capital at all, being but a 
manifestation of the fact that the total capital of the com- 
munity which he in part owns is also owned in part by 
others. Indeed, the phenomenon of credit means nothing 
more nor less than a specific form of divided ownership 
of wealth. Credit merely enables one man temporarily 
to control more wealth or property than he owns, that 
is, some part of the wealth or property of others. This 
occurs generally on the theory that he can use it to better 
advantage than the real owner. 

^ Palgrave's Dictionary of Political Economy, Vol. I, p. 452. 



Sec. 5] CAPITAL SUMMATION 97 

It is therefore a cardinal error to regard credit as in- 
creasing capital by the amount of that credit. Indirectly, 
credit may result in an increase of capital, through 
stimulating trade and production and by getting the 
management of capital into the right hands and its 
ownership into the most effective form; but the amount 
of any such increase of capital thus indirectly produced 
bears no necessary relation to the amount of the credit 
itself. If capital is increased, the credit does not constitute 
the increase, but merely represents a part ownership in the 
final total, after all the increments have been counted in. 

§5 

A great deal of confusion in legislation and writing could 
be avoided if the two methods of summing up capital were 
distinguished and their interrelations recognized. In taxa- 
tion, the two methods are often confused. A chief prob- 
lem of efficient taxation is how to tax all property once, 
and none of it more than once. There are two solutions : 
One is to tax the amount owned by each real person in a 
list which expresses the method of balances ; this method 
seeks out the real owners or part owners of wealth. The 
other is to tax the actual concrete wealth in a Ust which 
expresses the method of couples ; this method seeks out the 
real wealth owned. At present the two are much confused. 
Legislators too often fail to perceive that under the first, 
or owner-method, corporations should not be taxed, for 
they are not true owners; and that under the second, or 
wealth-method, bonds, stocks, and other part-rights to 
wealth should not be taxed, for these are sufficiently in- 
cluded when the actual railways and other wealth are taxed, 
which these securities represent. 

It is not claimed, of course, that a complete system of 
taxation can be worked out merely by choosing one of the 
two forms of taxes just indicated. We are here only con- 
cerned in pointing out that the distinction between the 



98 NATURE OF CAPITAL AND INCOME [Chap. VI 

two should be observed and that where one is applied the 
other cannot also be applied without duplicating the tax. 

The failure to distinguish clearly the methods of balances 
and couples also manifests itself in the form of fallacious 
statistics of capital. Statistics of railway capital have been 
compiled in which the value of all railway property is ob- 
tained by adding up the assets of the railways, regardless 
of the fact that many of these assets consist in stocks and 
bonds of other railways. 

We should therefore distinguish carefully the two meth- 
ods for the summation of capital, — one the method of 
balances, which exhibits capital as owned by different in- 
dividuals, and the other the method of couples, which 
exhibits capital as consisting of different concrete instru- 
ments. The one relates to the owner, the other to the 
things owned. They do not conflict, but present the same 
facts in different aspects. 



PART II. Income 

Chapter VII. Income 

Chapter VIII. Income Accounts 

Chapter IX. Income Summation 

Chapter X. Psychic Income 

Lora 



CHAPTER VII 

INCOME 



Income has already been defined as a flow through a 
period of time and not, like capital, as a fund at an instant 
of time, and as consisting of abstract services and not, 
like capital, of concrete wealth. The income from any instru- 
ment is thus the flow of services rendered by that 
instrument. The income of a community is the total flow of 
services from all its instruments. The income of an indi- 
vidual is the total flow of services yielded to him from his 
property. Before attempting to elaborate or even to justify 
this definition, we have first to examine the erroneous 
concepts of income now current. The present chapter is 
devoted to such an examination. 

It is no exaggeration to say that at present the state of | 
economic opinion on this important subject is deplorably I 
confused and conflicting. Many writers fail to construct 
any definition whatever, either because they find the task 
too difficult, or because they deem the concept too obvious 
to require definition. And those who do set themselves 
the task of reaching a working concept of income do not 
find it an easy one ; and authors often confess dissatisfac- 
tion with their own results. 

The definitions which are given are usually vague.* 
Their authors, often able and distinguished, and keenly 
alive to the difficulties of the subject, seem to take refuge 

^ F®r a collection of conflicting definitions see Appendix to Chap. 
VII, § 1. 

101 



102 NATURE OF CAPITAL AND INCOME [Chap. VII 

in an obscure and ambiguous phraseology.^ Were it not 
for an instinctive feeling that there exists a definite income- 
concept, the repeated failure to formulate it might lead one 
to conclude that it is not susceptible of any exact and rig- 
orous definition, and that the best course is to abandon its 
search as futile Kleinwachter, who wrote a book espe- 
cially devoted to this subject, specifically takes this course. 
He states that there is no useful concept of income,^ 
His idea is that, originally, merchants attempted to keep a 
record of their transactions by counting the money which 
they received and disbursed, and that, in consequence of 
this, arose the "illusory" notion that through some such 
record the complete economic standing of an individual or 
firm could be expressed. He observes, that such a com- 
plete picture could not be obtained by recording merely 
the incomings and outgoings of money, but should 
include Hkewise the incomings and outgoings of every other 
kind of wealth.^ A complete record, he states, would 
alone cover the required ground. So-called statistics of in- 
come are, he maintains, merely a makeshift for such a record.* 
But why should the possibility of a concept of income 
be rejected because it does not reveal a " complete" picture 
of an individual's economic condition ? On the same plea 
we might also reject the possibility of a concept of capital. 

^ E.g. F. Y. Edgeworth, Falgrave's Dictionary of Political Economy, 
article, "Income," Vol. II, p. 374: — 

" Income may be defined as the wealth, measured in money, which 
is at the disposal of an individual, or a community, per year or other 
unit of time." (The italics are the present writer's.) This formula- 
tion is adopted by N. G. Pierson, Principles of Economics, London 
(Macmillan), 1902, p. 76. 

^ Das EinJcommen und seine Verteilung, Leipzig, 1896, p. 11. 

^ Op. cit., p. 14. 

* The present writer at one time also expressed these doubts 
{Economic Journal, December, 1896, pp. 553, 554). By aid of the 
criticisms of Cannan and Edgeworth, the conclusions here stated were 
reached. These were first outlined in "Senses of Capital," Economic 
Journal, June, 1897, and in " The R61e of Capital in Economic 
Theory," Economic Journal, December, 1897. 



Sec. 2] INCOME 103 

A good definition should always conform to two tests: 
it must be useful for scientific analysis; and it must 
harmonize with popular and instinctive usage. We shall 
see that the usual definitions of income fail in one or both 
of these requisites. Many fail to lend themselves to scien- 
tific analysis by committing the fallacy of double counting, 
others by confusing income and capital, while almost all fail 
to harmonize with popular usage by making out income 
i larger or smaller than common sense would dictate. 

Like most familiar notions, the notion of income seems 
to the uninitiated clear enough without definition. But 
pitfalls which are unseen are for that very reason all the 
more dangerous. We shall point out a few of them by 
criticising, not the specific definitions of particular authors, 
but the general concepts of income which the reader is 
likely, more or less unconsciously, to have acquired. 

§2 

Q\ The concept of income which is the most common is 
that of "money-income." A business man's "money- 
income" means to him the money receipts from his busi- 
ness, less the money expenses of obtaining them. As 
applied to commercial affairs, this concept is nearly 
adequate, and in fact it coincides, as a special case, with the 
concept of income which we have adopted ; for the 
services which a man's business capital yields him usually 
consist exclusively of bringing him money, and the disserv- 
ices which it causes him, of taking money from him. Thus 
the net value of its services to him, or difference between 
the value of the services and disservices, is simply the 
difference between the money brought in and the money 
taken away from him by his business. 

But while the concept of "money-income" is correct so 
far as it goes, it is far from exhausting the complete in- 
come concept. As soon as we pass outside of commercial 
circles, we find cases in which money-receipts are evi- 



104 NATURE OF CAPITAL AND INCOME [Chap. VII 

dently only a part of all receipts and money-costs only 
a part of all costs. In primitive communities, and even in 
highly organized communities, the income of many persons 
consists; partly in the acquisition of goods other than 
money. /"The clergyman receives, besides his salary, the 
use of a parsonage ; and domestic servants receive, besides 
their wages, their food and lodging. Again, many goods 
considered as constituting income are not acquired by 
exchange at all, but produced by the individual himself. 
It is usually recognized that a farmer's income includes 
not only what he gets in money by sale and barter, but 
what he obtains "in kind," — the products of his farm 
consumed by his own family. 

On the other side of the ledger there are many costs 
which are not in money form, namely, sacrifices of com- 
modities and labor in the process of acquisition. The 
farmer's crops cost him labor as well as wages. Again, 
he may not pay money for his seed and fertilizer, but 
sacrifice for these some of the products of his farm 
instead. 

While the acknowledged existence of non-monetary re- 
ceipts and costs is of itself a sufficient proof of the in- 
adequacy of the money-income idea, there is the further 
objection that money-income itself exists, so far as it has 
any existence, merely for the purpose of purchasing 
other goods. The laborer's wages are not his "real wages," 
but the means to them. He transforms his money-wages 
into food, clothing, housing, and other uses. These, and 
not the money which buys them, constitute his real income. 
If we acknowledge this, we are led away from money- 
income to another concept common in economic litera- 
ture, but still inadequate, namely, "real income." 

§3 

"Real income" has been defined in various ways, and, 
like income in general, is often not defined at all. So 



Sec. 3] INCOME 105 

far as it has any recognized meaning, it may perhaps be 
expressed in the phrase "enjoyable commodities and serv- 
ices." This concept is certainly more adequate than 
that of money-income; for it includes the supplementary 
elements which we found lacking under the head of money- 
income, such as the clergyman's use of a parsonage, the 
servant's board and lodging, and the farmer's produce for 
his own consumption. It is also less superficial than the 
concept of money-income; for it recognizes that money 
is only an intermediary, and seeks to discover the real ele- 
ments for which that money-income stands. 

But the definition errs in two particulars : first, instead of 
making income consist simply and consistently of one kind 
of element, services, it attempts to include with this 
element the totally incongruous element, commodities; 
and, secondly, it unnecessarily restricts itself to enjoyable 
elements; for, though enjoyable elements are, in the last 
analysis, the final income of society or of an individual, 
the fact that they are should constitute the end of our rea- 
sonings and not the beginning. We shall now take up these 
two errors in order. 

That the two elements — "commodities" and "services" 
— form a heterogeneous combination is evident from the 
fact that one is concrete wealth and the other, abstract use 
of that wealth. To bring about homogeneity we could 
exclude uses altogether and confine "income" to concrete 
commodities ; or we could exclude commodities altogether 
and restrict the term whollj'' to uses. The latter alter- 
native, which is the solution offered in the present book, 
seems never to have occurred to those who have written 
on the subject. The former alternative is quite untenable 
and has been instinctively discarded. Instead of either 
alternative, the course which has actually been pursued has 
been the eclectic makeshift of including some commodities 
and the services or uses of others, and even sometimes both 
the commodities and the uses of these very commodities. 



106 NATURE OF CAPITAL AND INCOME [Chap. VII 

The choice of the commodities to be included has usually 
fallen on the less durable varieties, such as food, fuel, 
and clothing, while the objects the uses of which have been 
included have been the more durable instruments, 
such as dwelling-houses. In the case of intermediate types, 
such as carriages, furniture, and musical instruments, no 
fixed rule seems to have been observed. Some economists 
are inclined to regard a newly acquired piano as a part of 
real income, others to regard the music which comes from 
it as the real income, while still others apparently regard 
both the piano and its music as real income. Evidently 
such a patchwork of arbitrarily selected elements is in- 
capable of furnishing any consistent, reliable, and logical 
theory of income. 

§4 

The only true method, in our view, is to regard uniformly 
as income the service of a dwelling to its owner (shelter 
or money rental), the service of a piano (music), and 
the service of food (nourishment) ; and in the same uni- 
form manner to exclude alike from the category of income 
the dwelling, the piano, and even the food. These are capi- 
tal, not income; and the instant we include any such con- 
crete wealth under the head of income, that instant we begin 
to confuse capital and income. The newly purchased or 
newly constructed house is not an element of income, but 
of capital. The income appears afterward in the services 
the house yields its owner, — the shelter it affords through 
subsequent years or the bringing in of a money rent to its 
owner. In like manner the newly acquired piano and loaf 
of bread are not income, but capital. Their income fol- 
lows later in the form of piano music and nourishment. 

No reason has ever been given why the short-lived bread 
should be treated differently from the long-lived dwelling. 
The use of the bread is just as distinct from the bread as 
the use of the dwelling is distinct from the dwelling. The 



Sec. 4] INCOME 107 

difference between the case of the bread and that of the 
dwelling is purely one of degree. The uses of the bread fol- 
low the acquisition of the bread almost instantly, whereas 
the uses of the dwelling are not completely ended until 
many years after the dwelling is acquired. From this 
difference in time comes a corresponding difference in value. 
The value of the use of the bread is practically identical 
with the value of the bread. A man will give ten cents to- 
day for a loaf if he expects its use (consumption) to-morrow 
to be worth ten cents. The value of the dwelling, however, 
will be less than the value of its prospective uses, owing to 
the fact that these uses are so remote in the future. If 
the dwelling is expected to last fifty years, and its shelter 
to be worth $1000 a year, this $50,000 worth of shelter will 
not by any means be worth $50,000 in advance, but only, 
say, $15,000. This "capitalized" value of the expected 
uses of the dwelhng will be the value of the dwelling. In 
short, the bread and its uses are practically contemporane- 
ous and equal in value, whereas the dwelling and its uses 
are widely diverse in both particulars. Consequently it 
has not seemed worth while to economists to distinguish 
between the bread and its uses; whereas they could not 
help distinguishing between the dwelling and its uses. 

But in science, logical distinctions are inexorable, 
and their violation always brings retribution. It may 
be said in truth that if economists had been scrupu- 
lous enough to distinguish a loaf of bread from its uses, 
they would have escaped most of the confusions which 
have so long enveloped the theory of income. Having 
once chosen as the income element the food instead of its 
use, economists have proceeded to do the same in the case 
of clothing and other moderately durable commodities. 
Naturally they have not known where to cease calling the 
concrete instrument income and begin calling its use income 
instead. In their hesitation they have in some cases ended 
by including both. By so doing they commit the fallacy 



108 NATURE OF CAPITAL AND INCOME [Chap. VII 

of double counting. This fallacy they escape only in the 
case of the very durable instruments, such as the dwelling, 
and the very perishable instruments, such as the bread. 
The dwelUng is too evidently not income ever to be so 
regarded, and, as to bread, one of the two elements — its 
use — is overlooked altogether. But it is felt that inter- 
mediate types, like the piano, are as fairly entitled to be 
called income, when acquired, as the bread, and that their 
services are as fairly entitled to be called income as are the 
services of the dwelling. Consequently both are deemed 
income. But a piano valued at $500 is so valued because 
this sum is the capitalized value of the future expected 
uses which, let us say, are $600, distributed over the 
lifetime of the instrument. Consequently if, when the 
piano is first purchased, it is entered as real income to 
the extent of $500, and then later its subsequent services 
in providing its owner with music are also counted as 
income to the extent of $600, it is clear that there has 
been double (though successive) counting. The services 
of the piano have been counted as income in anticipation 
as well as in realization. 

Yet this error, in one form or another, is not infrequently 
committed. It is virtually in this way that Cannan ^ and 
others regard "savings" as income in the year in which 
the savings are accumulated, although the interest upon 
those savings will be counted as income in subsequent 
years. The nature of the fallacy is seen as soon as 
we translate from money to other instruments. If a 
man saves up money and purchases an automobile, 
it is clearly double counting to call the automobile thus ob- 
tained "real income," and then include its subsequent uses 
in the real income of ensuing years. It does not matter 

^ Elementary Political Economy, London, 1888, pp. 58, 59. The 
fallacy of including savings in income will be treated at greater 
length in Chap. XIV. The reader who believes that savings ought to 
be regarded as income is asked to stay judgment until he has finished 
Chap. XIV. 



Sec. 5] INCOME 109 

how durable the instrument; it is always double counting 
to include the instrument and its uses. The savings may 
be invested in land or in confectionery. The only true 
income is the use of the land or the use of the confec- 
tionery. To include also the value of the land or the 
value of the confectionery is to count as income the capi- 
taUzation of income. 

§5 

Economists have been more or less aware of the pitfall 
of double counting, but not of the reason for it. They 
have therefore attempted to avoid it, not by excluding all 
commodities from the income concept and restricting it to 
services, but by specifically excluding from income certain 
groups of commodities. Naturally, they have been at 
a loss to formulate a satisfactory and logical principle for 
this exclusion. Some of them have no better suggestion to 
offer than that all "large" or "unusual" acquisitions should 
be ruled out, and that only those commodities which come 
into a man's possession in a "regular" stream shall be en- 
titled to the name income. This makeshift has received 
much currency among German writers. To be sure, it 
serves the purpose of excluding from income such obvi- 
ously inappropriate elements as bequests and gifts of large 
fortunes. It is clear that when a well-known millionaire 
recently fell heir to seventy millions, this did not con- 
stitute his income for the year in which he received it, but 
that it merely constituted the principal or capital from 
which he would receive income in subsequent years. But 
the reason that it is improper to call this suddenly acquired 
fortune income is not that it was large, nor that it was 
sudden, but that it consisted of rights to concrete wealth 
— factories, ships, railways, and dwellings. These things 
are not under any circumstances income, but yield income 
through future uses. It is idle to call income "regular"; 
for we all know that it is irregular. 



110 NATURE OF CAPITAL AND INCOME [Chap. VII 

Another but very similar attempt to escape the difficulties 
of double counting and of confusing capital and income is 
to specify, not that income must in a vague way be "regu- 
lar," but that it must be such as to leave unimpaired the 
capital which yields it/ Such a definition has the merit 
of connecting income with capital as its source, but it merely 
shifts the pretended attribute of uniformity from the 
income itself to its parent capital. In actual fact it 
is seldom true either that income flows uniformly or that 
capital remains at a constant level. To stipulate such uni- 
formity as a necessary limitation of income is to define, not 
the actual irregular income which exists in fact, but an 
ideal standard which we set up for reference. It cannot 
be denied that the term "income" is sometimes used in the 
sense of such an ideal instead of in the sense of actual in- 
come ; and we shall follow this usage so far as to call such 
an ideal by the name of "standard income." What we 
insist on is that such standard income is not, and must not 
be confused with, the actual income which a man receives 
from his capital. It is simply the income which he would 
receive if he chose to keep his capital unimpaired and un- 
increased. If a man has his capital invested in the form of 
a house which yields him rent, this actual rent, less any 
actual expenses for repairs, taxes, etc., is his income 
from that house, even though the house may be depreciat- 
ing in value. The ideal or standard income whi h the house 
might yield without depreciation will be somewhat lower 
than this actual income, the difference being what is called 
amortization. 
^~{ This is not the place to discuss amortization and the rela- 
tions subsisting between standard and real income. These 
topics will be fully discussed in Chapter XIV. We are at 
present concerned with actual, not ideal, income; so 

1 This specification is characteristic of Hermann, SchmoUer, and 
many others. See Kleinwachter, Das Ei^kommen und seine Verteilung, 
pp. 22-23. 



Sec. 5] INCOME 111 

far as popular usage goes, it gives its sanction to the use of 
the term "income " in the one sense quite as much as in the 
other, though usually with very little intelligent discrimi- 
nation between the two. For instance, a life annuity from 
an insurance company, or a pension from a government, 
is universally recognized as "income." Yet this income 
trenches on the capital which produces it, eating it up year 
by year until, at the end of its allotted period, it is entirely 
exhausted. Let us suppose that the annuity is one of $1000 
a year for twenty years. Reckoning interest at five per cent, 
such an annuity is worth, by the actuaries' tables, $12,462. 
That is, the annuitant could sell his annuity, on a five 
per cent basis, for $12,462 in ready money. But this 
$12,462 invested at five per cent would bring in, with- 
out impairing the principal, not $1000 a year, but 
only $623.10. If then he actually gets $1000 he is 
trenching on his capital the first year to the extent of 
$376.90. Yet we regard him, and very properly too, as 
having a true income of $1000 a year. 

If it were true that income could never trench on capital, 
we could not reckon a laboring man's wages as income 
without first deducting a premium or sinking fund sufficient 
to provide for the continuance of this income after the de- 
struction by death of the laborer. If the annuitant or 
laborer should actually set aside such an annual sum as to 
maintain the capital value of his property unimpaired, we 
should be quite justified in considering the net sum, and 
not the gross sum, as income. The $1000 annuitant who 
pays $376.90 annually into a sinking fund is getting 
only $623.10 annually, not $1000, for an income, and the 
laboring man who pays an insurance premium reduces his 
income by that amount. '^-It surely makes a difference 
whether these "sinking funds" or "premiums" are actually 
set aside or merely reckoned. To reckon what one ought 
to save in order to maintain capital is not to save it, 
and a definition of income which depends upon an ideal 



112 NATURE OF CAPITAL AND INCOME [Chap. VII 

reckoning instead of a real payment is to that extent 
inadequate. 

§6 

We have now seen how the fatal inclusion of concrete 
wealth by the side of abstract services as a part of income 
has led economists into two errors, — one the confusion of 
capital with income, and the other the fallacy of double 
counting. We now proceed to consider the other mistake 
in the ordinary concept of real income, namely, that due 
to the needless restriction introduced by the term "enjoy- 
able." Real income, we were told, consists of "enjoyable 
commodities and services." We have thus far succeeded 
in eliminating "commodities" from this formula; we now 
proceed to show that we may also eliminate "enjoyable," 
and leave the very simple formula: Income consists of 
services. 

It is quite true that when we put together all the 
elements which go to make up the total income of a com- 
munity or of an individual, and deduct all the negative 
elements, or outgoes, we shall find that there are then left 
solely enjoyable services. But the various elements which 
are thus combined — the income from factories, mines, 
farms, and other instruments or groups of instruments — 
do not all consist of enjoyable services. Most of them 
consist of intermediate services preparatory to enjoyable 
services. How these intermediate services cancel them- 
selves out in the final summation will form the subject 
of a future chapter. At present we are merely concerned 
in pointing out that any adequate concept of income must 
leave room for these intermediate services, i.e. for the 
income rendered by a factory or a bank as well as that 
yielded by a dwelling or a pleasure yacht. We have already 
had occasion to note the inadequacy of that concept of 
income which restricts it to the yielding of money ; we now 
need to observe the inadequacy of that concept which 



Sec. 7] INCOME 113 

goes to the opposite extreme and leaves money income 
out of account altogether. Having found "money income " 
insufficient for their purposes, economists have conceived 
of "real income." But by making real income consist of 
"enjoyable" elements, they have excluded money income 
altogether. Some of them more or less avowedly retain 
both concepts, but they do not show how to coordinate them 
nor how to include them both under a more general income- 
concept. In their minds the two seem to stand totally dis- 
connected, except that, in a partial and incomplete way, 
real income is thought of as that for which money income 
is spent, 

§7 

The ordinary concepts of income fail to conform to any 
consistent scheme whatever. In consequence, among other 
needless distinctions, are those which have been drawn 
between social and individual income. 

Social income has usually been conceived as the "net 
product" of society, — not in the sense of the net difference 
between services and disservices, but in a sense which 
includes commodities. No consistent method of reckoning 
this net product has been furnished. It is clear that we 
cannot include all products. Some are only too evidently 
new capital, such as newly constructed railways, steam- 
ships, tunnels, bridges, and buildings and would not be 
included by most persons in social income. Others must 
certainly be omitted to avoid duplication in our reckoning. 
If we were to include the wheat crop of the farmer, the 
flour of the miller, and the bread of the baker, we would 
be counting the same thing three times over, — once for 
each of three successive processes. Some economists have 
sought to avoid this repetition, either by excluding the pro- 
duction and consumption of raw materials, or, if these are 
included, by not including the whole value ol the finished 
product, but only the increment of value over that of the 
raw materials. 



114 NATURE OF CAPITAL AND INCOME [Chap. VII 

"We must be careful not to count the same thing twice. If we 
have counted a carpet at its full value, we have already counted the 
values of the yarn and the labour that were used in making it; and 
these must not be counted again. But if the carpet is cleaned by 
domestic servants or at steam scouring works, the value of the labour 
spent in cleaning it must be counted separately; for otherwise the 
results of this labour would be altogether omitted from the inventory 
of those newly-produced commodities and conveniences which consti- 
tute the real income of the country." ^ 

These reservations are entirely correct; but they fur- 
nish no general means of avoiding double counting. For 
instance, are fuel and labor to be deducted in the same 
way as raw materials ? Some writers have gone so far as 
to claim that, just as the cost of feeding work animals 
must be deducted from the value of the work they do, so 
the cost of supporting laborers must be deducted from the 
value of their product.^ If this view were correct, it would 
seem that the laborer could not share at all in the distri- 
bution of the social income, since all that comes to him 
is deducted ! 

A similar question as to deductions arises in the oft- 
cited case where one profession is more disagreeable or 
irksome than another. Should any deduction be made 
from the income of the hangman, for instance, to equalize 
his net income with the net income of a more desirable 
calling ? 

When social income is called "net product," the same 
question arises which was met with in the case of individual 
income, viz., whether by "product" is meant concrete 
wealth, or services, or both. In our own theory, " services " 
are taken, but the usual concepts adopt wealth, or both 
wealth and services. According to them, part of the in- 
come of society consists of new wealth, such as factories, 
sihps, and dwellings, while the services of these new creations 

1 Marshall, Principles of Economics, Vol. I, p. 150. 

^ E.g. "Report of Committee on a Common Measure of Value in 
Direct Taxation," Report of British Association for Advancement of 
Science, 1878, p. 220. 



Sec. 7] INCOME 115 

figure as income in future years. We have already observed 
that to count a new dwelHng or piano as income this year, 
and its use as income in succeeding years, is a species of 
double counting as well as a confusion of capital and income. 
Both of these errors are repeated in any concept of social 
income which includes at once additions to the world's 
wealth, and the income which this very wealth subse- 
quently yields. 

§8 
When a wrong road is once taken, it almost inevitably 
happens that it leads those who follow it further and fur- 
ther astray. Economists, having selected a wrong idea 
of income to start with, naturally found it so ill suited to 
their purposes that, in each problem to which they at- 
tempted to apply it, some special interpretation or amend- 
ment became necessary, until, instead of one concept, 
they became possessed of a miscellaneous assortment^ of 
concepts ! They have been compelled not only to dis- 
sociate money-income and real-income, but also to disso- 
ciate the income of the individual and the income of society. 
When it is understood that the entire and only contribution 
to the income stream which any given instrument of capital 
can make consists in the services which that instrument 
renders, it will be found that all subsidiary meanings of 
income are simply incomes from particular instruments 
or groups of instruments. If the instrument in question is a 
private carriage, the services which it brings forth, as events 
desirable to its owner, are the acts of conveying him from 
one place to another. These are primary or natural-incouie. 
If the in trument is a public carriage, the services which it 
brings forth, as events desirable to its owner, are the pay- 
ments of fares. These are money-mcoiaej' If the group of 

^ The reader who cares to study them in detail will find a collec- 
tion of definitions in the Appendix to Chapter VII. 

^ It should be borne in mind that the income is not the money 
itself, which is a concrete commodity, but the bringing in of the 
money, which is an abstract service. 



116 NATURE OP CAPITAL AND INCOME [Chap. VII 

instruments is the entire group of instruments constituting 
the entire capital of a community, the net total of their 
services and disservices is the entire income of the com- 
munity. This is social income. If the group be the entire 
property of an individual — the rights which he owns, 
complete or partial, in instruments — the net total of the 
services and disservices to which he is thus entitled consti- 
tutes his income. This is individual income. 

In science, the chief test of a definition is its adaptability 
to analysis. Judged by this test, none of the current con- 
cepts of income which we have passed in review can 
claim to be adequate ; for we have found them subject to 
the confusions of capital and income, and of double count- 
ing. A secondary test is that a working definition should 
also fit into, or rather, give clear and consistent outlines 
to the vague notions of income which we find ready made in 
the actual world of business and accounts. 

Of our own concept of income, as consisting exclusively 
of services, we shall endeavor to show that it includes the 
commercial bookkeeper's concept of "money income"; 
that it is coextensive with the popular notions of income, 
including what those notions include and excluding what 
they exclude ; that it affords a place for the usage by which 
sinking funds are reckoned and justifies the phrase "living 
beyond income"; that it avoids double counting auto- 
matically and without the necessity for the exercise of judg- 
ment in each special case ; that it makes capital and income 
strictly correlative but never in danger of being confused; 
and last, but not least, that it lends itself readily to economic 
analysis and serves as a foundation for the theory of interest. 

The concept of income to be elaborated is similar to 
several which have been put forward by other writers. 
It is almost identical with that of Edwin Cannan ; ^ it 

^ See History of the Theory of Production and Distribution ; Elemen- 
tary Political Economy; and "What is Capital?" Economic Journal, 
1837. 



Sec. 8J INCOME 117 

also harmonizes with what Professor Marshall ^ calls 
the "usance" of wealth, and with the psychological 
concepts of income in President Hadley's Economics^ in 
Professor Flux's Economic Principles,^ and in Professor 
Fetter's Principles of Economics.* Finally, it harmonizes 
more closely than at first glance might be supposed, with 
the etymological and popular meaning of income. In- 
come from any source is what comes in from that source. 
The income from any capital is what that capital brings in 
to its owner, no matter what may be the form of benefit 
brought in. If the capital serves to bring in money, the 
income is ''money-income." If it serves to bring in crops 
or products, as does a self-supporting farm, the income is 
of another form. If it serves to bring in enjoyable com- 
forts, as does a dwelling house, the income is of a still 
different form. But in all cases, the essential fact is that 
the capital performs service, — accomplishes something 
desired. 

As this usage makes income include all money-income, it 
cannot be maintained that it conflicts with commercial 
usage. It may be objected by the unreflecting that by 
including non-monetary elements it includes too much; 
but many — often all — of the non-monetary benefits con- 
ferred by capital are recognized as income by economists, 
as well as by such men of affairs as have studied the 
subject with care. A business man who had bought a 
yacht remarked: "It's a good investment, and I get my 
dividends every Saturday afternoon when I take a sail in 
it." And the writer has never had any difficulty in per- 
suading other business men of the propriety of such usage. 
In fact, without an enjoyable use in prospect, money-income 
itself would have no existence or meaning. A house could 

^ See Principles of Economics, 3d ed. (Macmillan), Vol. I, p. 156. 
A part of this passage is quoted in Appendix to Chap. VII. See also 
Carver's Distribution of Wealth (New York, Macmillan, 1904), p. 123. 

2 Chap. I. 3 p_ i7_ 4 pp 43^ 571^ 



118 NATURE OF CAPITAL AND INCOME [Chap. VII 

never command a money rent to the landlord if it did 
not also 3deld shelter to the tenant, and even from the 
standpoint of the landlord the receipt of the money only 
intervenes as a medium for payment of his own rent and 
other expenses of living, in other words for securing his 
enjoyable income. 

Income is, then, a very general concept. It consists of 
services rendered by capital. We have seen that under it 
are included several special concepts : Social income, indi- 
vidual income, money income, natural income, and enjoyable 
income. We shall soon see that the net income of society 
or of an individual consists wholly of enjoyable income. 
This is because the non-enjoyable elements of income, 
such, for example, as money-income, are all exactly offset 
by equal items of outgo. But the non-enjoyable elements 
are none the less a part in the grand total, and, in fact, 
by far the greater part. The money-income of ordinary 
bookkeeping forms the bulk of any true inventory of in- 
come; but its significance cannot be understood until its 
counterpart in outgo is also taken into account, nor until, 
in fact, a complete picture of all elements of income is 
brought before the mind's eye. To present this picture 
will be the object of the next three chapters. 



CHAPTER VIII 

INCOME ACCOUNTS 



The income of our capital, then, is simply that which 
it does for us. Whether it brings us money or other return 
does not matter; the flow of its services is its income. 
These services of wealth, as was previously explained, con- 
sist of any desirable events which occur by means of that 
wealth or any undesirable events prevented. 

Services exist in infinite variety. All work done by 
human beings, all the operations of industry, all the trans- 
actions of commerce, are services, and enter into income 
accounts. A bird's-eye view of this busy planet would reveal 
wealth — real estate, commodities, and human beings, — 
ceaselessly at work performing services. Land, men, and 
implements are changing land, seed, and live stock into 
grain, beef, lumber, and steel. Manufacturing plants are 
converting raw materials into flour, furniture, cloth, and 
implements. In domestic establishments we find the serv- 
ices of cooking, warming, cleaning, and sheltering. Agri- 
culture, mining, transportation, and commerce are simply 
names that we give to the group of services performed by 
farm, mine, railroad, and business capital. 

A disservice is a negative service. It is an undesirable 
event occasioned, or a desirable one prevented, by means of 
an article of wealth. A flow of disservices or negative in- 
come is called outgo. It does not matter whether the outgo 
occasioned by an article consists in depriving the owner 
of money or in some other evil. If the outgo is in mone- 

119 



120 NATURE OF CAPITAL AND INCOME [Chap. VIII 

tary form it is called expense; if it is in the form of human 
exertion it is called labor. It includes all of what economists 
have called cost, i.e. labor, trouble, expense, and sacrifices of 
all kinds. 

An instrument very seldom yields services without in- 
volving some disservices. A dwelling house, for instance, 
not only gives off services called shelter, but also occasions 
disservices in the form of labor (or expense) for renewals, 
painting, cleaning, caretaking, insurance, and taxes. Any 
disagreeable event occasioned by that house is a disservice; 
just as any agreeable event is a service. Again, while 
a saddle horse performs services in giving its owner a 
daily ride, it performs disservices in being stabled, fed, 
and shod. A farmer gets services out of his land when it 
yields him crops; but to get these services he has to put 
fertilizer, seed, labor, and expense into that land. A rail- 
way performs a vast service of transportation, hauling 
passengers and commodities, but it requires a prodigious 
amount of coal, suppHes, and labor to keep it going. 

Disservices are not essential to the idea of wealth; an 
article of wealth sometimes offers services without any dis- 
services. When disservices exist they are usually over- 
balanced, in the estimation of the owner, by prospective 
services. As soon as the disservices of an article of wealth 
preponderate, in the est mation of its owner, over the serv- 
ices, it is regarded as "more trouble than it is worth," 
is cast aside and ceases to be wealth. In the meantime 
such articles, if regarded as owned at all, constitute a 
sort of wealth of negative utiUty, — Jevons calls them 
"discommodities." They are never of great importance 
and need receive no special attention. The chief examples 
of such articles are garbage, ashes, sewage, carrion, rubbish, 
and waste. 

It has already been observed that services and disserv- 
ices, hke wealth, are measured in two ways — in quantity 
and value — and that the quantity of each service is 



Sec. 2] INCOME ACCOUNTS 121 

measured in its own special unit. The quantity of the serv- 
ices of a gardener is often measured by the number of 
hours he works ; the services of a windmill, by the number 
of gallons of water pumped. Quantities of services (or 
disservices) are thus, like instruments of wealth, very hetero- 
geneous and are incapable of being combined in a single sum. 
To obtain a homogeneous mass of value, we must multiply 
the quantity of services (or disservices) by their several 
prices. 

Income and outgo, then, like capital, are used in two 
senses: income-services (as well as outgo-disservices) and 
income-value (as well as outgo-value). Hereafter, when 
the terms "income" or "outgo" are used alone, the value 
sense will be understood. 

The value of any individual service or disservice con- 
stitutes an element of income or outgo. The value of all 
the services flowing from an article of wealth through any 
period, that is, the sum of all the elements of income, is 
called its gross income^ '-The excess of the gross income 
over the outgo, in other words, the algebraic or net sum 
of all elements of income and outgo, is the net income. If, 
instead of an excess, there is a deficiency, it is called net 
outgo. Net income is of far more impoi^tance, both in 
practice and in theory, than gross income;|- Gross income 
may often be measured in more than one way, according 
as the elements of which it is composed are considered 
with or without accompanying olBFsets ; but the sum called 
net income will be the same in either case. 

§2 

Income (or outgo) always implies (1) capital as the 
source, and (2) an owner of capital as the beneficiary. 
Mr. Smith's income from his farm imphes that the farm 
yields the income and that Mr. Smith receives it. In this 
book we shall need to consider income chiefly in its rela- 
tion to the capital yielding it rather than in its relation to 



122 NATURE OF CAPITAL AND INCOME [Chap. VIII 

the owner receiving it.^ This twofold aspect of income is 
expressed in accounts by regarding the farm as "in account 
with " its owner. All income from it to him is placed on one 
side of the ledger and is said to be "credited" to the farm, 
while its outgo is, in Hke manner, "debited." A credit 
item, then, signifies income which is yielded by a given 
capital, and a debit item signifies outgo which it occasions. 
The terms refer respectively to positive and negative ele- 
ments in the income and outgo accounts of that capital. 

We are now in a position to apply the foregoing defini- 
tions to income accounts. We begin by imagining a "house 
and lot" as an article of wealth or capital, and shall first 
consider its income and outgo during the period of the cal- 
endar year 1900. The income which this capital brings 
in to its owner may be either a money rental or the serv- 
ices of shelter for himself and family. In either case the 
income may be measured in money, although in the case of 
occupancy by the owner this measurement requires a special 
appraisement. We shall suppose that the house was built 
many years ago and in 1900 is nearly worn out. It yields 
an income worth $1000 a year. Against this income there 
are offsets in the form of repairs, taxes, etc. ; for these pay- 
ments are "undesirable events" occasioned by the house 
and lot. We have, then, the following "income account" : 

Income for House and Lot during Year 1900 

Income Outgo 

Use of house and lot . . $1000 Repairs $200 

Taxes 100 

Insurance 100 

$1000 $400 

The net income is therefore $600. 

1 The terms income and outgo are somewhat unfortunate, as, 
etymologically, they suggest the relation to the owner Smith rather 
than to its source, the farm. Smith's income is the farm's "out- 
come"or "yield" (in German, ertrag). Similarly, when the farmer 



Sec. 2] INCOME ACCOUNTS 123 

Next year we may suppose that the house is found to 
have rotted beams, is condemned, and must be abandoned 
or torn down. Its services are ended, but the land is still 
good and the owner can build a new house. This operation 
consmnes, let us say, the first six months of the year 1901, 
so that during that period there is no income, but only outgo. 
During the second half of the year the house is occupied and 
its use is valued at $600. In the first six months not only 
did the "house and lot" fail to yield any income, but on the 
contrary occasioned an expense. The cost of production of 
the house was a disservice; for this was an "undesirable 
event" occasioned by the house and lot. It was withstood 
only for the sake of future services which it would bring in 
its wake. It was not itself a desirable event. When we 
say, then, that any event is undesirable, we make ab- 
straction of future compensations. All disservices are 
"necessary evils"; they lead to good, but are themselves 
evils. 

We have, then, the following account : — 

Income for House and Lot during Year 1901 

Income Outgo 

Use of house and lot (six Expense of building 

months) $600 house $10,000 

Taxes 100 



$600 $10,100 

During this year, then, the house yields a net outgo of $9500. 
This adverse balance will be more than made up in the years 
which follow. For the year 1902 we may have the fol- 
lowing : — 

puts fertilizers on his land, this, his outgo, is the farm's ingo. But, 
although we shall be largely concerned with income and outgo in 
relation to capital as their source, and might therefore logically 
employ the terms outcome and ingo, it seems preferable, for reasons 
of usage, to retain the usual terms, income and outgo. 



124 NATURE OF CAPITAL AND INCOME [Chap. VIII 

Income for House and Lot during Year 1902 

Income Outgo 

Use $1200 Repairs $ 50 

Taxes 150 



$1200 $200 



Net income .... $1000 

Let US suppose that these figures remain about the same 
for forty-nine years, and give $50,000 net income dur- 
ing that time, which cancels the excess in cost for 1901 
of $9500 and leaves a large margin besides, the nature 
of which, as interest, need not here be considered. Then a 
second time the house is worn out and has to be rebuilt. 
The same cycle is repeated, one year of excess of cost being 
offset by forty-nine years of excess of income. 

§3 

^ It will be observed that the cost of reconstructing the 
house was entered in the accounts in exactly the same way 
as repairs or other "current" costs. There may seem to 
be objection to such a proceeding in the thought that recon- 
struction appears to be not a part of "running expense" 
but a "capital cost," and belongs, not to income accounts, 
but to capital accounts. It is true that the value of the 
new house must be entered on the capital balance sheet, 
but the cost of "producing it belongs properly to income 
accounts. The former represents wealth; the latter repre- 
sents disservices. The former relates to an instant of time 
(which may be any instant from the time it is begun till 
the time when it ceases to exist) ; the latter relates to a 
period of time (which may be all or any part of the time 
during which the labor and other sacrifices occasioned by 
the house occur). A house is quite distinct from the 
series of sacrifices by which it was fashioned. The con- 
fusion between the two is natural in view of the practice 



Sec, 3] INCOME ACCOUNTS 125 

of bookkeepers in often entering capital at its " cost value." 
In fact it is sometimes said that "liabilities represent money 
received by a company, and assets, how it has been ex- 
pended." But this is not strictly true. Since its market 
value depends on its suitabihty to the uses to which it is 
put, not on the money sunk in its construction, the house on 
which was expended $10,000 for construction may be worth 
more or less than $10,000. In this case the income 
account should contain $10,000 on the outgo side, and 
tlie capital account should contain a larger or smaller 
figure.^ 

And yet it is undoubtedly true that we instinctively 
object to entering the cost of building the house in its 
income-and-outgo account; and we express this objection 
by calling this cost a "capital cost," rather than a part of 
running expenses. By so classing it we mean that it does 
not recur, or, at any rate, only at long intervals. 'On this 
basis Wagner and others have erroneously claimed that 
income and outgo should be confined to "regular" items. 
At first glance this seems feasible because, in actual prac- 
tice, an extraordinary expense in a given year, like the 
cost of constructing a house, does not usually reduce the 
owner's net income for that year by that amount. He will 
generally contrive to avoid such a result by offsetting 
the extraordinary expense of the house by a correspond- 
ingly extraordinary income from some other source, such 
as a depreciation fund. It is evident that the house owner 

^ Even in the normal case the value of the house, as is well known, 
is not exactly equal to the cost expended in construction, but to that 
amount plus interest. A house which costs $10,000, expended through 
six months, ought to be worth a few hundred dollars more than this 
sum at the time of completion ; otherwise the man who expended those 
$10,000, and at completion has only $10,000 worth of house to show 
for it, has evidently received no interest on his money. The relation 
between the value of capital, and its cost, and interest, will form a 
subject to be taken up in a later chapter, where the common error 
that accrued, but unpaid, interest is itself a cost will also be dis- 
cussed. 



126 NATURE OF CAPITAL AND INCOME [Chap. VIII 

who has had the foresight to set aside annually throughout 
the period of existence of the house a small deposit in a 
savings bank, may derive therefrom, when the time for 
rebuilding arrives, a large sum of money, the receipt of 
which is just as properly an element of income as its 
expenditure for rebuilding is an element of outgo. The 
great outgo for rebuilding is then offset by a great income 
from the savings bank account, so that the combined net 
income from the two sources — depreciation fund and 
house — will be approximately zero and the total net in- 
come of the individual will be affected little or not at all. 
The depreciation fund, therefore, does not prevent, but 
merely offsets the large negative balance in the income 
account from the "house and lot" considered by itself. 
The combined income from the two sources taken together 
will be negligible, but that from the one source, the "house 
and lot," will fluctuate. In figures, from this single source, 
the net income is evidently +11000 a year for each of forty- 
nine years, and —$9500 for the fiftieth year <X It is mislead- 
ing to say that the $1000 is "gross" income from which must 
be deducted the depreciation fund or "amortization" sup- 
posed to be laid aside each year against the cost of rebuild- 
ing. Merely to suppose a depreciation fund is not to have 
one. It is quite true that the $1000 income which the house 
yields during each of forty-nine years is more than the income 
which would have been left after an annual payment into 
a depreciation fund had actually been made; but an income 
which simply might have been is only an ideal standard. 
Confusing the actual and the ideal is one of the commonest 
fallacies in this field. The actual net income of the house 
and lot is alone the object of our present study, and this 
actual income, in the example we are supposing, is $1000 
each year for forty-nine years. While this sum is in excess 
of the ideal standard income during each of these forty- 
nine years, this overplus is atoned for by the sudden and 
large deficiency every fiftieth year. 



Sec. 4] INCOME ACCOUNTS 127 

§4 

Such irregularity of income may be avoided, not only 
by a depreciation fund, but by other devices, for instance, 
by paying for the house in installments, by borrowing 
money to defray cost and mortgaging the house, or by sell- 
ing other property. Another method of steadying income 

— and one which ought to set at rest any remaining qualms 
which the reader may feel at the procedure, which has been 
adopted, of entering cost of new construction under "outgo" 

— applies when the same owner possesses so many of the 
articles in question that the reconstruction of one or another 
of them must occur at short intervals. Consider, for in- 
stance, the case of a building and loan association which 
has fifty houses, each built in a different year and each of 
which lasts fifty years, so that the houses have to be 
rebuilt at the rate of one every year. In the accounts of 
such an association the expense side should include the 
cost of new construction as a regular annual item, thus : — 

Building and Loan Association 
Fifty houses (with land) 1900 
Income Outgo 

Rents of 49 houses at Construction of one new 

$1000 a year . . . $49,000 house $10,000 

Rent of one house for Repairs on 49 houses . 4,900 

part of the year in Taxes 5,000 

which it is constructed 500 



$49,500 $19,900 



Net income .... $29,600 

We have here a net annual income of $29,600, which con- 
tinues year after year without interruption. The irregu- 
larity of income which we found in the case of a single house 
ceases when the larger number is taken. But if it is proper 
to regard the cost of reconstructing the houses as outgo 
in the case of a large number of houses, it must be equally 



128 NATURE OF CAPITAL AND INCOME [Chap. VIII 

proper to regard it as outgo in the case of each single house ; 
for the income account of the total mass of the commu- 
nity's capital is simply the combined accounts of the 
individual elements. We cannot consistently do other- 
wise than regard all costs, whether recurrent or not, as 
outgo. 

In actual business there are usually many articles of 
the same kind, so that it is seldom necessary to reckon the 
net income from each individual article. Such articles may 
be conveniently lumped together. This we have just seen 
in the case of the houses of the loan association. As an- 
other example we may take the stock-in-trade of a mer- 
chant. This stock yields him income, not, as in the case 
of the house, by rent, but by sale ; the difference between 
rent and sale being simply that rent consists of a series of 
contributions to income, whereas sale consists only of one. 
A stock of stoves, just as a stock of houses, yields income 
which is the sum of the net incomes from its individual 
constituents. But the stove dealer would find the book- 
keeping very troublesome were he to reckon in a separate 
account the net income from each individual stove which 
he buys and sells. He reaches the same final result for 
his stock as a whole (or rather, for each specific category 
of articles in his stock) by taking from his gross receipts 
obtained by selhng stoves the year's cost of replenishing 
his stock, the rent of his warehouse, salaries of clerks, and 
other outgo. Were he to arrive at this result by applying 
the same process to each individual stove, the individual 
results would, of course, vary widely ; for a stove left over 
from last year (and therefore free from any item of cost 
in this year's accounts), if sold this year, would give a 
large net income, while another stove, bought this year, 
but not sold until next, would only have debit items in 
this year's account. But the sum of these irregular 
incomes from individual parts of the merchant's stock 
will give a steady income for the whole. 



Sec. 5] INCOME ACCOUNTS 129 

Any merchant's stock that rapidly changes the individual 
elements of which it is constituted is most conveniently 
treated as a whole. To use Professor Clark's admirable 
simile, it is like Niagara Falls, which remains a waterfall, 
although consisting each day of entirely different drops of 
water. The stock of a butcher, grocer, or fruiterer consists 
of rapidly changing elements, but remains as a whole 
relatively unchanged. Though it would be logically sound, 
it would be foolish and impracticable to keep an income 
and outgo account for each individual leg of mutton or 
box of figs. The tendency to-day, however, is distinctly 
toward a more detailed accounting. Some business firms, 
by means of modern card indices, keep a careful record for 
each separate variety of commodity dealt with, if not for 
each individual article in that variety. The important 
thing to observe is that the net income of the entire group 
is simply the difference between the sums of the incomes 
and outgoes of the elementary units which constitute that 
group. The very item which, for the elementary unit, 
constitutes "capital" cost, and which, for that unit, occurs 
but once, becomes, for the group, the regular cost of re- 
plenishing, and recurs annually. From the explanations 
and illustrations which have been given, it is clear that 
consistency and logic must assign to every cost, whether 
large or small, regular or irregular, a place as an element of 
outgo in the income-and-outgo accounts, 

§5 

Whether or not the irregularities of income from indi- 
vidual articles of wealth are smoothed away in the total, 
the combined income, even from a large group of articles, 
is not necessarily an absolutely steady flow. We usually 
strive to make it so to some extent ; but we do not always 
succeed, nor do we even always try. When income does 
vary, the method of measuring which has been given will 
unerringly register that variation automatically. The 



130 NATURE OF CAPITAL AND INCOME [Chap. VIII 

method is not, of course, restricted to a group of articles 
of the same kind, hke the fifty houses of the building and 
loan association or the stock of stoves of the stove dealer. 
It appUes to any stock of miscellaneous articles, and even 
to the entire stock of wealth of a community or the world. 
The net income from any such group is simply the sum of 
the net incomes of the various articles of wealth in exist- 
ence at all the points of time within the period for which 
that income is reckoned. 

In hke manner may be obtained the income from any 
collection of property rights as capital. This application 
of income-and-outgo accounts occurs especially in the case 
of an individual. For we then find that the sources of 
income consist largely, not of capital-wealth, but of capi- 
tal-property, — partial rights to wealth, such as bonds, 
stocks, and mortgages. But the introduction of the idea 
of property as distinct from that of wealth involves no new 
difficulties ; for we have seen that property is only another 
aspect of wealth, and represents simply rights to some of 
the services of wealth. Thus in respect to partnership 
rights, each partner in the firm of Smith & Jones, farmers, 
receives half the income of the farm. The same principle 
applies in respect to shares, bonds, or other forms of prop- 
erty. Business men are accustomed to say that a railway 
bond yields or earns so much income. But this merely 
means that the railway behind this bond yields income, a 
specified share of which belongs to the bondholder. Thus 
the true source of the services which flow to the property 
holder is the concrete wealth; his property-right merely 
specifies such portion of those services as are his. The 
income of a stockholder, for instance, consists of all the 
benefits he receives from being a stockholder, less all the 
sacrifices. Usually, for him, both benefits and sacrifices 
accrue in monetary form. His income from his stock is 
usually the receipt of dividends. 

The total net income of a person is, then, the sum of 



Sec. 6] INCOME ACCOUNTS 131 

the net incomes from each individual article of property 
which he holds within the time interval considered. 

§6 

To illustrate this, let us consider the case of a lawyer 
hving in a rented house, but owning the furniture. We 
shall assume, for simplicity, that his property is grouped 
under the following nine heads: (1) stocks and bonds, 
(2) lease of house (including not only the privilege of occu- 
pancy but also the obligation to pay rent), (3) furniture 
of house, (4) other household supplies, especially food, 
(5) money and bank account, (6) claim on servants (includ- 
ing not only the claim on their work but also the obligation 
to pay wages), (7) like claims on, coupled with obligations 
from, office clerks, (8) his own person, (9) " etc." We 
shall take, as the time interval, a period of a month. 

During the month, the stocks and bonds bring in checks 
aggregating $2,000 and the lawyer buys new securities to 
the extent of $500. His total net income, therefore, dur- 
ing this particular month from this particular group of 
property rights is $1500. Under his lease he enjoys a 
month's use of a house, this use being regarded by him as 
worth, let us say, exactly what it costs, or $100 a rnonth. 
Since the lease yields him $100 worth of shelter and costs 
him $100 in money, it leaves no net income. His furni- 
ture yields him comfort worth $50, from which cost of 
repairs, etc., amounting to $30, has to be deducted, leav- 
ing a balance of $20. His stock of food and similar sup- 
pUes yields him the board of himself and family for the 
month, worth $150 ; but the cost of replenishing this stock 
and the services of cook and waitress in preparing and 
serving it absorb, let us say, all of this sum, leaving for 
the month no net income from the pantry's stock. 

The next source of income (or outgo) is " cash." By 
this is meant the stock of property which includes money 
on hand and money on deposit in bank. To find how 



132 NATURE OF CAPITAL AND INCOME [Chap. VIII 

much income or outgo comes from " cash " we need only 
follow the well-established usage of bookkeepers which 
regards a stock of cash as though it were a gold mine 
which, consequently, is to be credited with all the gold or 
cash which comes out of it, and debited with all that goes 
into it. This usage often puzzles the novice, but its cor- 
rectness is undoubted and it harmonizes with our defini- 
tion of services and disservices. For the services or 
desirable events which come from one's stock of cash — 
the events, in fact, for the sake of which that stock of 
cash exists — are the furnishing of money from time to 
time ; the disservices, or the undesirable events occasioned 
by that stock of cash, are the absorption by it of money 
from time to time. In other words, my purse serves me 
whenever it pays my bills ; it costs me whenever I, so to 
speak, pay its bills. In this respect it is precisely similar 
to any other stock of wealth. A bin of coal serves its owner 
when it renders him fuel; it costs him when it has to be 
filled. The cost may be the sacrifice of money, of labor, or 
of coal taken from some other store of coal. In the case 
before us, the income from "cash," or all the payments the 
lawyer takes out of his pocket-book or check book, amounts, 
let us say, to $3780, whereas the outgo to "cash" — all 
sums paid to it — amounts to $4000, leaving $220 as a 
net outgo. 

The claim on the servants, like the lease of the house, 
involves an obligation to pay as well as a right to receive. 
We shall suppose that the servants render services during 
the month worth $100, and also cost $100 in wages, leav- 
ing no net balance. Similarly the office clerks cost $500 
in wages and yield $500 worth of assistance to the lawyer 
in the preparation of his cases. 

The man himself receives from his practice during the 
month $2000. But his office and professional expenses 
amount to $500 and leave a balance of $1500. The class 
called "etc." comprises all sources of income not other- 



Sec. 6] 



INCOME ACCOUNTS 



133 



wise included, such as clothing, watches, jewelry, and other 
articles of wealth or property not contained in the other 
categories. For simplicity we shall suppose that the in- 
come and outgo connected with '' etc." are equal to each 
other, and amount to $2500. 

The total income of this man is therefore as follows : — 



Income, 


Outgo 


Net 
Income 










Profit and 










Loss 


By stocks and bonds 




To stocks and bonds 






(money) .... 


$2000 


(money) 


$ 500 


+ 11500 


By lease right (shelter) 


100 


To lease right (money) 


100 


00 


By furniture (use) . . 


50 


To furniture (money) 

To food (money (50) 

and work of serv- 


30 


+ 20 


By food (use) . . . 


150 


ants (100) .... 


150 


00 


By "cash" (money) . 


3780 


To " cash " (money) . 


4000 


- 220 


By servants (services) 


100 


To servants (money) 


100 


00 


By clerks (personal as- 










sistance) .... 


500 


To clerks (money) . . 
To self (assistance of 


500 


00 


By self (money) . . 


2000 


clerks) (money) 


500 


+ 1500 


By "etc." (direct uses) 


2500 


To "etc." (money) . 


2500 


00 




Total net income . 


-h$2800 



These accounts may be simplified in various ways, and 
without any sacrifice of logical completeness. If we are 
interested only in the total net income, and not in the share 
which each item of property contributes to this total, we 
may omit several items which in the above accounting stand 
on both sides. For instance, the cooking and serving food 
was debited to the stock of food and credited to the servants. 
At first sight it may appear that the wages of cook and 
waitress are entered as debit both to "servants" and to 
"food" and that double counting has occurred. But the 
debit to food was not servants' wages but servants' work. 



134 NATURE OF CAPITAL AND INCOME [Chap. VIII 

A little consideration will show that if we credit the servants 
with the services of cooking and waiting, and debit them 
with wages as a distinct item, we must debit the food 
with their services of cooking and waiting. If we prefer 
to drop out these services both from the credit side of the 
servants' account and the debit side of the food account, 
we are then at liberty to omit the category of servants 
entirely, and to leave only the charge of their wages 
against the food. There are endless admissible modifica- 
tions of the accounting here described, many of which 
have practical advantages, but the preceding is pre- 
sented as a complete and detailed record of all income and 
outgo arranged by sources. 



In complete accounting we must not omit the negative 
items of property, or liabilities. The same principles 
apply here as for positive items, or assets. Items which 
are negative are such because they yield negative income, 
or outgo. If the lawyer whose accounts we have followed 
is in debt, the payments on his debt (whether "interest" 
or "principal") which he makes during the time-interval 
considered are outgo. On the other hand, if a debt is 
contracted during the time-interval considered, its pro- 
ceeds are for that period an addition to gross income. 

Thus an income-and-outgo account may always be com- 
pletely formed by recording the values of the services and 
disservices occasioned by all the articles of capital under 
consideration. In the case of an individual these articles 
of capital are his assets and his liabilities. No other items 
than the services and disservices mentioned can properly 
find a place in the accounts. We have already warned 
the reader against the fallacy of deducting from income 
any depletion of capital; he should also be warned 
against the opposite fallacy of adding to income any sav- 
ings of capital. This fallacy is so common and so subtle 



Sec. 8] INCOME ACCOUNTS 135 

that its discussion will be postponed to Chapter XIV, 
where it may receive the attention it deserves. We con- 
tent ourselves at present with a preliminary illustration. 
/.'-A savings bank depositor is sometimes thought to draw 
income from his deposit when the interest "accumulates." 
This is an error. He draws income when, and only when, 
he draws money out of the bank; he suffers outgo when, 
and only when, he puts money into it. If he merely lets 
his deposit accumulate, he derives no income and suffers 
no outgo. There is no effect on income. What does occur 
is increase of capital. He cannot have his cake and eat it 
too. If we make the fiction that the man who allows his 
savings to accumulate virtually receives the interest, we 
must, to be consistent, also make the fiction that he rede- 
posits it. If the teller hands over the interest across the 
counter, the depositor's account certainly yields up "in- 
come" to him, but if he hands it back it must, in consist- 
ency, be charged as "outgo," and the net result on his 
income is simply a cancellation. This procedure reveals 
clearly the fact that the accumulation is not income. _^ 

§8 

The method of accounting employed in the preceding 
lawyer's account is, of course, not the only, nor is it the 
usual, method. It is the method, however, which shows 
the shares of the total income attributable to each indi- 
vidual source. In practice, the minor sources of income 
are neglected. The income and outgo of one's " cash " 
almost balance in the long run, and the same is true of 
the lease, the servants' contracts, and the household sup- 
plies. One's furniture probably yields a larger net income 
than is commonly realized, but even this is usually a small 
element in the total. It is only in case the lawyer lives in 
his own house that a serious correction would need to be made 
on this account. In this case, his shelter is not offset by 
any rent payment, and enters the accounts as pure income. 



136 



NATURE OF CAPITAL AND INCOME [Chap. VIII 



Practically, therefore, the lawyer's income is obtained 
by taking from the above table only the two principal 
items, the income from investments and the income from 
his professional work. Each of these is $1500, so that 
according to this approximate accomiting the net income 
is $3000. Another and more common method of approxi- 
mating an income account is to record simply money 
receipts and disbursements, in other words, to record 
only the items of the preceding account under "cash." 
The lawyer's cash account book would present an appear- 
ance like the following : — 



Receipts 

From stocks and bonds 
From personal labor . 



2000 



Investments, in 

and bonds 
Rent .... 
Furniture repairs 
Cost of food 
Servants . . . 
Clerk hire . . 
"Etc." . . . 



Disbursements 

stocks 



$4000 



$ 500 

100 

30 

50 

100 

500 

2500 

$3780 



This leaves a cash balance of $220, which is to be added, 
at the end of the month, to the cash on hand at the begin- 
ning. This balance does not here indicate the net income 
of the lawyer, as did the balance in the completer account- 
ing which preceded. The net income of the lawyer, in the 
incomplete and makeshift accounting now under consid- 
eration, is, so far as it is represented at all, shown in the 
total cash receipts less certain makeshift corrections. The 
justification of such accounting, so far as any exists, is that 
most income, from whatever source, passes through the 
cash drawer. 

It will be noticed that the receipts side of the above 
account, $4000, greatly exceeds the true net income, 
$2800, shown in the previous accounting. Instinctively 
any one using such mere money accounting feels the need 



Sec. 8] INCOME ACCOUNTS 137 

of making some deductions from the total money receipts. 
He also instinctively feels that not all of the disbursements 
should be thus deducted ; otherwise little or nothing would 
remain. The ordinary makeshift is to deduct the " business 
expenses," — the $500 invested in stocks and bonds and 
the $500 for clerk hire. The remainder will then be 
$3000, which is, for practical purposes, a sufficiently close 
approximation to the true net income of $2800. 

Practically, therefore, either money receipts (less "busi- 
ness" expenses) or the sum of the net incomes from secu- 
rities and labor, are good makeshifts for true income. But 
even from a practical point of view they will not always 
serve, while as a matter of strict theory they are always 
wrong. They could be right only under the condition that 
all income, from whatever source, flowed through the cash 
drawer. If it were true that the net income from stocks and 
bonds, the net income from the lawyer's practice, and, in 
like manner, the net income from every other source flowed 
into the cash drawer, while, on the other hand, the flow out 
of that drawer consisted exclusively of expenditures for 
each and every satisfaction as it occurred, then the flow of 
money through the cash drawer would serve as a true meas- 
ure of income, and the cash drawer might be called a sort of 
income meter. The flow into it would be money income 
and the eventual satisfactions obtained from it would be 
real income. The two would then also have the relation 
usually ascribed to them by economists. This case is 
practically reahzed in the case of a rentier, who simply re- 
ceives money from investments and spends it for imme- 
diate satisfactions, renting, let us say, not only a dwelling 
but its furniture as well, so that practically no part of his 
income can reach him except by passing through the money 
stage. But few people are in exactly this position, so that 
not all income passes through the meter. Some passes 
around it, as, for instance, the shelter derived from a man's 
own house or the comforts from his own furniture, and hence 



138 NATURE OF CAPITAL AND INCOME [Chap. VIII 

will not be registered by the meter at all. On the other 
hand, some passes through it not toward direct satisfactions 
but toward some "business" expenditure likely later on to 
repour cash through the money meter and hence to cause 
it to register too much. Thus it happens that the money 
meter sometimes fails to register and sometimes registers 
twice. It is therefore only a rough and imperfect instru- 
ment for measuring net income. 

§9 

^ When we turn from real to fictitious persons, we find, for 
income accounts, as for capital accounts, that the two sides 
necessarily balance exactly. A corporation, as an entity 
distinct from its stockholders, cannot enjoy income or 
suffer outgo. All the income not devoted to other ex- 
penses is absorbed in paying dividends. ; A railway com- 
pany, for instance, has an income account as follows : — 

Income Account op Railroad Corporation for Year 

Income Outgo 

By passenger and To operating ex- 
freight service . $1,246,147 pense's $800,000 

To interest to bond- 
holders .... 100,000 
To dividends to stock- 
holders 200,000 

To surplus applied to 

(1) purchase of 

land .... 140,000 

(2) cash in treasury 6,1^7 



$1,246,147 $1,246,147 

In these accounts we see that the gross income from all 
sources was $1,246,147, of which $800,000 disappeared for 
running expenses, $100,000 for paying bondholders, and 
$200,000 for paying stockholders, leaving a balancing item 
of $146,147. But this balance is likewise expended, $140,- 
000 of it being outgo for new land, and the small odd sum 



Sec. 10] INCOME ACCOUNTS 139 

$6147 being put into the safes of the company or deposited 
in bank. Even this last operation is a true outgo; for a 
cash drawer and a bank account are, as we have seen, always 
debited with what is put into them. There remains, there- 
fore, no final balance for the abstraction called the "com- 
pany." Just as, in the capital accounts, the company's 
excess of assets over liabilities to other than stockholders 
constitutes the true liability to the stockholders themselves, 
so, in income accounts, any excess of income over outgo to 
other purposes than dividends paid to stockholders con- 
stitutes a true outgo for the benefit of those stockholders. 

§10 

We see, then, that the guiding principle for the construc- 
tion of the income account, either of real or fictitious per- 
sons, is simply to make a complete list of the services and 
disservices which flow from each and every item of the assets 
and liabilities. This simple relation between capital and 
income accounts is commonly obscured by the fact that it 
is not practically convenient to include in one's capital ac- 
counts certain items of assets and Uabilities, although their 
services and disservices are entered in the income account. 
This is true, in particular, of one's own person, and such 
claims as are coupled with equal obligations, as leases and 
contracts with laborers. These are not and, from a purely 
practical point of view, ought not to be entered in the 
capital account ; but much of the income and outgo from 
them, such as wages and rent, are entered in the income 
account. In respect of income accounts the use of one's 
dwelling is omitted, as well as the unpaid-for services and 
disservices of human beings. A shopkeeper usually keeps 
a punctilious record of the work of his employees, but sel- 
dom any of his own personal work. If he owns the build- 
ing he occupies, he will not usually include its use in his 
accounts. In private life he seldom or never includes in 
his accounts the use of furniture. 



140 NATURE OF CAPITAL AND INCOME [Chap. VIII 

Our present object, however, is to show, not the methods 
of practical bookkeeping, but merely the application of 
economic principles to such bookkeeping. The chief ob- 
ject is to find the philosophical basis of accounting. Care- 
ful examination shows that accounting is at bottom not a 
mere makeshift but a complete, consistent, and logical sys- 
tem. When thus conceived and understood it will be seen 
to be of importance, not alone to the accountant but also to 
the economist. For his purposes, the only method of con- 
structing income and outgo accounts which is philosophic- 
ally correct, and which can serve as a basis for economic 
analysis, is the method by which are recorded, for each 
article of capital, the values of all its services and disserv- 
ices. These services and disservices are of many kinds. 
Sometimes they consist of money payments, sometimes of 
productive operations, and sometimes of enjoyable ele- 
ments. These all enter the accounts on the same footing, 
but in the next chapter we shall see that after being thus 
entered, the items may be so combined that all except the 
enjoyable elements will cancel among themselves. 



CHAPTER IX 

INCOME SUMMATION 



We have now seen how to reckon the income of either a 
real or a fictitious person. By combining the net incomes 
of all persons, the net income of society may be obtained. 
As we have seen, fictitious persons have no net income, 
and would therefore not affect such a method of summation. 
Another way to obtain the total social income is by adding 
together the net incomes from each individual article of 
concrete capital, regardless of its ownership. In such a 
summation no partial property-rights, such as stocks and 
bonds, would appear. Instead we would only find actual 
railways, mills, refineries, and other concrete capital. For 
instance, the net income earned by the Southern Pacific 
Railroad, considered as an aggregate of roadbed, termi- 
nals, rolling stock, and other existing instruments, would 
be taken. This would not be the income of the Southern 
Pacific Railroad Company, for, as we have seen, the com- 
pany, as such, has no net income. Nor would it be the 
income of the stockholders of the company, for this con- 
stitutes only a part of the earnings of the road. Nor 
would it be exactly the sum of the incomes of the stock- 
holders and bondholders, inasmuch as the company may 
earn income from other sources than the railroad itself, as, 
for instance, through leases of other roads and shares held 
in other companies, none of which income is produced by 
the railway. It would be simply the difference between 
the total value of the services of transportation rendered 

141 



142 NATURE OF CAPITAL AND INCOME [Chap. IX 

by the railroad and the value of the disservices occasioned 
by it, whether through cost of operation, repairs, renewals, 
or betterments. 

The two ways of obtaining the total social income which 
have just been outlined — (1) by summing the net incomes 
of individual persons as owners, and (2) by summing the net 
incomes from individual articles of wealth as sources — may 
be illustrated by supposing two ledgers to be opened con- 
taining the income for a given community, one ledger 
being devoted to each way. Each page of Ledger No. 1 
would be devoted to the income-account of a particular 
individual, stating in detail, in two columns, the items of 
income and outgo in the minute manner already shown. 
In Ledger No. 2 likewise each page would be devoted to 
the income-account of a particular article of wealth. The 
first ledger would represent, therefore, the distribution of 
income among different persons in the community. The 
summary of such a ledger, arranged according to the mag- 
nitude of the incomes, would give us the "distribution 
curve" of incomes shown by Professor Pareto.^ 

Let us suppose, for the sake of illustration, that the fol- 
lowing is such a summary for the United States : — 

Distribution Ledger No. 1 

Net Income for 1900 

15,000 millionaire families $ 2,000,000,000 

100,000 families, incomes ranging from $10,000 to 

$50,000 3,000,000,000 

1,000,000 families, incomes $1000 to $10,000 . . 5,000,000,000 
20,000,000 families below $1000 10,000,000,000 

$20,000,000,000 

The second ledger would show the same total income, 
but distributed according to the source which produced it. 
We may suppose a summary of Ledger No. 2 to be as 
follows : — 

^ See his Cours d'Economie Politique, Lausanne, 1897, Vol. II, pp. 
299-345. 



Sec. 2] INCOME SUMMATION 143 

Distribution Ledger No. 2 

Net Income for 1900 

From land $ 2,000,000,000 

" buildings 2,000,000,000 

" railways and tramways 1,000,000,000 

" factories 1,000,000,000 

" persons 13,000,000,000 

" etc 1,000,000,000 



$20,000,000,000 

§2 

Both these ledgers would be constructed by combining a 
number of separate net incomes, each one of which was the 
balance remaining after deducting the outgo from the gross 
income of the particular group of capital considered. In 
other words, both ledgers would be constructed — to adopt 
the phrase which was employed under capital accounts — 
by the "method of balances." 

But there is also a second method of summing incomes, — 
the "method of couples." Just as the same item in capital 
accounts is both asset and liability, according to the point of 
view, and is, therefore, self-canceling, so the same item in 
income accounts is both service and disservice, and is, there- 
fore, also self-canceUng. The reader may, in fact, have felt 
that, in many of the examples cited, what we called dis- 
services seemed to him to be services. He may have asked 
himself. Why should we call rebuilding a house a disservice ? 
When a carpenter and his tools repair it, do we not credit 
him and them with services? Is not any production a 
service? Are not, then, repairs placed on the wrong side 
of the ledger ? In answer it may be said that when a car- 
penter with his plane, hammer, and saw helps to rebuild a 
house, we have to consider two groups of capital. One 
group, the carpenter and tools, is acting on the other group, 
the house. The carpenter and tools used in the process 
certainly perform a service, but the house does not. Con- 
sidered as occasioned by the hoiise, the repairs are dis- 
services. The house absorbs or soaks up these costs. 



144 NATURE OF CAPITAL AND INCOME [Chap. IX 

promising to compensate for them by better service later 
on. Tiie renailing of loose shingles is certainly not what 
the house is for, but is only a necessary evil. On the part 
of the hammer, however, these same events are services. 
The service called " nailing " is credited to the hammer. 
Therefore the repairing of the house is at once a service 
and a disservice. 

Such double-faced events require a special name. We 
may christen them interactions between two instruments 
or groups of instruments. Alternative names are inter- 
acting services, intermediate, or preparatory services, 
coupled services, or simply "couples." They underlie 
what business men call "double entry bookkeeping." 

An interaction, then, is a service of the acting instrument, 
a disservice of the instrument acted on. There can never 
arise the shghtest doubt as to when it is to be regarded as 
positive and when negative. The definitions of service and 
disservice settle this question in each case, by referring it 
to the desire of a human being, viz. the owner of the service 
or disservice. As he desires that the house should not occa- 
sion repairs, these repairs are disservices of the house; as 
he desires that the tools should occasion repairs, they are 
services of those tools. The hammer exists for and derives 
its value from its prospective services in renailing shingles. 
The house does not exist for nor derive its value from the 
renailing of its shingles; on the contrary, the prospect of 
that event detracts from its value. 

The example given is typical of the general relations 
between interacting instruments. The mental picture we 
should construct is that of two distinct groups of capital. 
Group A acts on group B for the benefit of the latter. 
Whatever the nature of this interaction, A is credited with it 
and B debited. The credit and debit are equal and simul- 
taneous, the only result of the interaction being that, in 
consequence of it, B is enabled at some later time to yield 
more income. 



Sec. 3] INCOME SUMMATION 145 

Interactions are essentially identical with what were dis- 
cussed a generation ago under the title "productive serv- 
ices." But inasmuch as the name "productive services" 
is not a very happy one, and its use has been so confused and 
has engendered so many verbal quibbles, it seems advisable 
not to revive it. The essential fact that these "productive 
services" were two-faced — negative as well as positive — 
was always overlooked, and there remained no other charac- 
teristic which could give the phrase a definite and scientific 
meaning. 

Interactions constitute the great majority of the elements 
which enter into income and outgo accounts. The only 
services which are not merely the positive side of interac- 
tions are mental satisfactions — desirable conscious experi- 
ences — often miscalled "consumption"; and the only 
disservices which are not the negative side of interactions 
are pains or "labor." But these are only the outer fringes 
of the economic fabric. Between them is a connective net- 
work of productive processes and commercial transactions, 
every fiber of which has two sides, a positive side of serv- 
ices and a negative side of disservices. 

§3 

The interactions between two articles or groups of articles 
may, of course, consist either in causing or preventing 
changes or events. The events or changes which are 
caused or prevented are of three chief kinds, — changes of 
form of wealth, changes of position, and changes of owner- 
ship ; or, transformation, transportation, and transfer. We 
shall take these up in order. 

What is here called transformation of wealth is prac- 
tically identical with what is usually understood by "pro- 
duction" or "productive processes." ^ By the transforma- 
tion of wealth, or the changes produced in its form, is 
meant the changes of relative position of its parts. Weav- 

^ Cf. Marshall, Principles of Economics, 3d ed., p. 132. 



146 NATURE OF CAPITAL AND INCOME [Chap. IX 

ing, for instance, is the transformation of yarn into cloth 
by a rearrangement in the relative position of the warp and 
woof. Spinning, likewise, consists of moving, stretching, 
and twisting fibers into yarn ; sewing, of changing the posi- 
tion of thread so that it may hold cloth together; and so 
with carding, wool-sorting, shearing, and all the other 
operations which constitute the manufactm-e of fabrics. 

All manufacture and agriculture consist simply of a 
series of transformations of wealth, and each transformation 
is two-faced. On the part of the transformed instrument 
(or instruments) the transformation is a disservice ; on the 
part of the transforming instrument (or instruments) it is a 
service. We have seen that when a carpenter and his tools 
transform a house, i.e. build or repair it, he and his tools 
are credited and the house is debited. The same is true 
when the painter decorates it or the janitor cleans it. 
When a cobbler transforms leather into shoes, he is per- 
forming services; the shoes at each stage are occasioning 
disservices, or costs. When a bootblack transforms dirty 
shoes into clean and polished ones, he Hkewise is rendering 
services, and the shoes, disservices. In like manner, a loom 
which produces cloth out of yarn is to be credited with this 
operation as income, while the stock of cloth receiving the 
product of the loom is to be debited with the very same item 
as part of its outgo or "cost of production," 

Again, land renders a service in producing wheat. On 
the part of the wheat, however, this is a disservice. Wheat 
production is a service of land, a disservice *of wheat. If 
we consider a farm as pouring its crop into the stock of 
wheat of a granary, the entry of wheat from farm to wheat 
stock is credited to the farm as its service and debited to the 
wheat stock as its disservice. 

Sometimes, as has been said, the interaction consists not 
in causing a change, but in preventing one. A warehouse 
renders its service as a means of storing bales of cotton, i.e. 
protecting them from the elements. This storage is, how- 



Sec, 3] INCOME SUMMATION 147 

ever, on the part of the stock of cotton, an element of outgo 
or expense. 

As has already been intimated, there may be, and usually 
are, more articles than one in either or both of the two 
interacting capitals. Plowing, or the transformation of 
land into a furrowed form, is performed by a plow, a horse, 
and a man. The plowing is a cost debited to the land on 
the one hand, and at the same time a service credited to 
the group of capital consisting of the plow, horse, and man 
on the other. We are not here concerned with the problem 
of how much should be placed to the credit of each co- 
operating agent, but merely with the fact that the sum 
total of the three is equal to the debit for the land. 

The principle is not altered if one or more of the trans- 
forming agents perishes and another comes for the first time 
into existence in the transformation. Bread-baking is a 
transformation debited to the bread and credited to the 
cook, the range, the flour, and the fuel, of which the last 
two perish as soon as they perform their services. Agents 
which disappear in the transformation but reappear, in 
whole or in part, in the product are called "raw materials." 
The production of cloth from yarn is a transformation ef- 
fected by means, not only of the loom, but also of a number 
of other agents, and among them the yarn itself. The cost 
of weaving includes as cost the consumption of raw material, 
yarn, and this consumption of yarn, on the part of the 
yarn itself, is not cost or disservice, but service. It is 
the event for which the yarn had existed. When cloth 
is turned into clothes this transformation is a service to 
be credited to the cloth, and a disservice to be debited to the 
clothes. All raw materials yield services as they are con- 
verted into finished products. Their conversion is, however, 
always outgo on the part of those products. 

In this way, when an article passes through various stages 
of production, it is often an arbitrary matter whether we 
designate those stages by different names or not. A "sap- 



148 NATURE OF CAPITAL AND INCOME [Chap. IX 

ling" grows into a "tree." We may, if we choose, consider 
the sapUng as one category and the tree as another. In 
this case the "sapUng" performs a service at the moment 
it becomes a "tree," just as the "tree" performs one later 
when it, in turn, becomes "lumber"; but no effect on 
social income is produced, because, if we credit the sapUng 
with the value of the tree, we must debit the tree with the 
cost of the sapling. Likewise we may arbitrarily designate 
the moment when a "calf" becomes a "cow," or when 
"new" wine becomes "old," without disturbing the income 
accounts of society; for such events are always two-faced 
and cancel themselves out in the total. We may, in fact, 
mark any stage whatever in the course of production by an 
arbitrary Une, and regard the passage across this Hne as a 
service on the part of the capital on one side of the line 
and a disservice on the part of the capital on the other side. 

§4 

The second class of interactions is transportation, or the 
change in place of wealth. It is a very thin Hne which 
separates this class from the preceding class. Transform- 
ing or producing wealth consists of changing the position 
of its parts relatively to each other ; transporting wealth 
is changing the position of that wealth as a whole. But 
"part" and "whole" are themselves loose and relative 
terms. Bookbinding is a transformation or production of 
wealth; it assembles the paper, leather, thread, and paste 
into a whole book. Delivering books to a library is trans- 
portation. Yet the library is, in a sense, a whole ; and to 
assemble books into a classified and organized Ubrary is to 
make a whole out of parts. The distinction between trans- 
formation and transportation is thus merely one of conven- 
ience. Many writers prefer to include them both under 
"production." We prefer to include them under the less 
ambiguous and more inclusive rubric "interactions," and 
our object here is not to emphasize their difference, but 



Sec. 5] INCOME SUMMATION 149 

their similarity. The same principle of equal and opposite 
services appUes to both. When merchandise is changed 
from one warehouse to another, the first warehouse is 
credited with the change and the second debited. The 
warehouse which has rendered up the merchandise has 
done a service; that which has received it has done a 
disservice. A banker who takes money from his vault and 
puts it in his till will, if he keeps separate accounts for the 
two, credit the vault and debit the till. When wheat is 
imported from Canada, that nation is credited and the 
United States is debited with the value of the operation. 
We may, as in the case of continuous productive pro- 
cesses, divide up transportation districts by any arbitrary 
lines, and consider the passage of any articles across those 
lines as an interaction. 

§5 
The third class of interactions is the change of owner- 
ship of wealth or property. This has been called transfer. 
Transfers usually occur in pairs, and involve two objects 
transferred in opposite directions between two owners. 
This double transfer, we have called an exchange. Since 
an exchange consists of two transfers, and since a transfer 
is a species of interaction and as such is self-canceling, 
every exchange is self-canceling and cannot of itself con- 
tribute anything to the total income of society.^ When a 
bookseller, for instance, sells a book, he credits his stock 
with the fact that it has brought in money, and the cus- 
tomer debits his Hbrary to the same amount. 

1 The exchange does not dupHcate income, but merely shuffles it 
about. It may and does put services of wealth where they are most 
needed, and thus results in a more effective use of income, just as 
credit and other forms of the divided ownership of wealth may make 
a more effective ownership of capital. In both these cases there is an 
increase of "total utility." This needs to be considered in its proper 
place, but it must not stand in the way of our canceling the values 
of assets and liabilities or of services and disservices. These values, 
as is well known, are connected, not with total utilities, but with mar- 
ginal utilities. 



150 NATURE OF CAPITAL AND INCOME [Chap. IX 

These two items constitute the transfer between the 
stock of books of the dealer and the stock of books of the 
customer. The remaining two items constitute a transfer 
between the stocks of cash of the two men; the dealer 
debits his " cash " and the customer credits his. 

When therefore an article of wealth changes hands, 
it occasions an element of income to the seller and an 
element of outgo to the purchaser, and therefore no income 
at all to society. The effect of canceling these items — 
the credit item of the seller and the debit item of the pur- 
chaser — is to free the income account of that article from 
all entanglements with exchange, to wipe out all money- 
income, and to leave exposed to view what we have called 
the natural income of the article. Thus, books yield their 
natural income, not when the book dealer sells them, but 
when the reader peruses them. The sale is a mere pre- 
paratory service, a credit item to the book dealer and a 
debit item to the buyer. The fact of bookselling adds 
nothing to the income of society, but the reading of the 
book does. Again, a forest of trees yields no natural 
income, until the trees are felled and pass into then ext 
stage of logs. The owner of the forest may, to be sure, 
"reaUze" on the forest long before it is ready to be cut, 
by simply selling it to another ; and to him the forest has 
then yielded income ; but, as the purchaser has suffered an 
equal outgo, the forest has as yet yielded nothing to society. 

The principle that an article of capital yields, to society, 
no income except its natural income, is not altered when 
its ownership is divided nor when the part rights are 
bought and sold. Adam Smith regarded a rented house 
as bearing income in the form of rent, but a house occu- 
pied by the owner as bearing no income at all. The truth 
is nearly the reverse. Both houses yield income, and both 
incomes are of the same kind, viz. shelter. The rent of the 
rented house is, for society, not income at all. It is income 
to the landlord but outgo to the tenant, — outgo which he 



Sec. 5] INCOME SUMMATION 151 

is willing to suffer solely because of the shelter he receives. 
This shelter alone remains as the income from the house 
after the rent transaction is canceled out between the two 
parties concerned. The shelter-income is the essential and 
abiding item, and without it there could be no rent-income 
to the landlord. 

Again, a railway yields as its income solely the natural 
one of transporting goods and passengers. Its owners sell 
this transportation service for money and regard the rail- 
way simply as a money maker; but to the shippers and 
passengers this same money is an expense and exactly off- 
sets the railway's money earnings. Of the three items — 
money income of the road, money outgo of its patrons, 
and transportation — the first two mutually cancel and 
leave only the third, transportation, as the real contribu- 
tion of the railway to the sum total of income. 

We see, then, that the method of couples, applied to 
buyer and seller, denudes all capital of its so-called 
"money-income," and lays bare the only income it can 
really produce, the natural income. We see that capital 
is not a money-making machine, but that its income to 
society is simply its services of production, transporta- 
tion, and gratification. The income from the farm is the 
yielding of its crops ; from the mine, the production of its 
ore; from the factory, its transformation of raw into fin- 
ished products; from commercial capital, its passage of 
goods from producer to consumer; from articles in con- 
sumers' hands, their enjoyment or so-called " consumption." 

Similar principles apply to outgo, no part of which, for 
society, exists in money form. The great bulk of what mer- 
chants call "cost of production," expense, or outgo, consists 
of money costs which carry with them their own cancella- 
tion. For manufacturers, merchants, and other business 
men, almost every outgo is an expense, i.e. consists of a 
money payment. Such money payments are for wages, 
raw materials, rent, and interest charges. Now all these 



152 NATURE OF CAPITAL AND INCOME [Chap. IX 

outgoes are incomes for other people. The wages are the 
earnings of labor; the payment for raw material is re- 
ceived by some other manufacturer ; the rent by the land- 
lord; the interest charges by the creditor. 

§6 

Not only do exchange transactions completely cancel 
themselves out in reckoning total income, but the great 
majority of the natural services of capital do so also. 
Even these natural uses of capital consist, for the 
most part, of "interactions," — they are transformations 
or transportations of wealth. These intermediate stages 
are merely preparatory to the final use or so-called "con- 
sumption" of wealth, and, after the interactions have been 
canceled out, do not enter as items either on the income 
or outgo side of the social balance sheet. 

In order to show the effect of canceUng out the equal 
and opposite items entering into every interaction 
throughout the productive processes, let us observe the 
various stages of production which begin with the forest 
above referred to. The product of the forest, its gross in- 
come, is the series of events called the turning out of logs. 
This log-production is a mere preparatory service, a credit 
item to the forest and a debit item to the stock of logs of 
the saw mill, to which they next pass. As the sawmill 
turns its logs into lumber, the lumber yard is debited with 
the production of lumber, and the sawmill is credited with 
its share in this transformation. 

Intermediate categories may, of course, be created, and 
we may follow, in like manner, the further transformation, 
transportation, and exchange to the end of the stages of 
production, or rather, to the ends ; for these stages split up 
and form several streams flowing in different directions. 
To indicate merely one of these streams, let us suppose that 
the lumber which goes out from the yard is used in repairing 
a certain warehouse. The warehouse is used for storing 



Sec. 6] INCOME SUMMATION 153 

cloth; the cloth goes from the warehouse to the tailor; 
the tailor converts the cloth into suits for his customers; and 
his customers receive and wear those suits. In this series, all 
the intermediate services cancel out in "couples" and leave 
as the only uncanceled element, or final fringe of services, 
the use of clothes in consumers' hands. 

Should we stop our accounts, however, at earlier points 
in the series, the uncanceled fringe will be not consumers' 
services, but the positive side of intermediate services or 
interactions. The negative side will not appear, as it be- 
longs to later stages in the series. This will all be clear, if 
we put the matter in figures, stage by stage. The follow- 
ing are the items for the logging camp above mentioned, 
in the accounts of its owner : — 

Income Account for Logging Camp for Year 1900 
Income Outgo 

Production of logs $50,000 (Omitted) 

The gross income from the logging camp, considered by 
itself, and without any deductions for expenses, is here seen 
to consist in the production of $50,000 worth of logs. If, 
however, we combine the logging camp with the sawmill, we 
shall have accounts like the following, in which, to avoid 
irrelevant complications, no account is taken of any ex- 
penses which are not interactions between the groups of 
capital considered : — 

Income Account for Logging Camp and Sawmill for 1900 



Capital Source 



Logging camp 
Sawmill 



Income 



Yielding logs to 

sawmill . . . $50,000 
Yielding lumber 

to lumber yard $60,000 



Outgo 



Receiving logs 
from camp . $50,000 



154 NATURE OF CAPITAL AND INCOME [Chap. IX 

In this case, canceling the two log items we have left only 
the lumber item; i.e. the income from the combined logging 
camp and sawmill consists only of the production of lumber, 
its final product. The transfer of logs from one department 
to the other no longer appears. This transfer is hke the 
taking of money from one pocket and putting it in another, 
as is particularly evident m case the logging camp and 
sawmill are combined under the same management. 

Extending the same principles to the entire series, we have 
the accounts as given on the opposite page. 

It should be noted that these entries relate not to suc- 
cessive but to simultaneous events ; that all the items refer 
to a fixed period of time; that is to say, we are not following 
the fortunes of the original logs through succeeding stages, 
but comparing the simultaneous operations of the series of 
groups of instruments. 

If we successively cancel items pair by pair by offset- 
ting any item on the right side by the item in the line 
above it on the left side, we shall find, if we stop after the 
first two cancellations, that the net income from logging 
camp, sawmill, and lumber yard, consists only of the pro- 
duction of retail lumber, $70,000 ; it does not include either 
the transfer of logs or the transfer of wholesale lumber. In 
like manner, if we proceed one stage further, that is, if we 
stop our cancellations, at the end of the first four interac- 
tions, the production of retail lumber no longer appears as 
an element of income ; and so on, step by step to the end, 
when the only surviving item will be the " wear " of the 
suits. 

It is, of course, true that in any actual accounts there 
will be numerous other items than those which have been 
exhibited in this simple chainlike fashion. Were it worth 
while, we might insert these additional entries of income 
and outgo elements. Most of them would consist of the posi- 
tive or negative side of an interaction, and if we were to 
introduce its mate, the opposite aspect of the same transac- 



\ 



Sec. 6] 



INCOME SUMMATION 



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156 NATURE OF CAPITAL AND INCOME [Chap. IX 

tion, it would be necessary to include still other accounts. 
If we should follow up all such leads we should soon have an 
intricate network of related accounts. But the same prin- 
ciple of the interaction as a self-effacing element would apply. 
The only items of outgo which are not the negative sides of 
interactions will be the items of subjective labor and 
trouble. These alone will finally remain as uncanceled 
elements of outgo. 



The table given will throw light on the question, Of what 
does income consist? The question is not a thoroughly 
definite one. If we ask instead, Of what does the income 
from a particular group of capital consist ? we shall make it 
definite. Whether the production of logs is income or not 
depends upon the point of view. It is income from the 
first link of capital (logging camp) in our series ; it is not 
income from the first two links combined, for in the second 
link it occurs as outgo. Likewise, the use of the ware- 
house is true income with respect to the first four links 
or groups of capital, but is no longer income when the fifth 
is included. 

We see, therefore, that the income from any group of 
capital does not consist in any degree of the interactions 
taking place within it, but only of the final or outer fringe 
of services performed by the group. As the group is en- 
larged, this particular outer fringe disappears by being 
joined to the next part of the economic fabric, and another 
frmge, still more remote, appears. The question naturally 
arises. When is the economic fabric complete, and has it any 
final outer fringe ? But this question must be deferred for 
the present. 

Nor do we yet inquire what relations exist between the 
two sides of the same account, say the expense to the saw- 
mill for logs and its income from sawn lumber. In the illus- 
trative tables the latter is entered as greater than the 



Sec. 8] 



INCOME SUMMATION 



157 



former, and this is normally the case, if the capital of the 
sawmill remains constant. At present, however, we are 
not concerned with the effects of income and outgo on 
capital, but only with the summation of income. 



The method of couples, then, is useful in showing of 
what elements income consists in any given case. The 
method of balances, on the other hand, exhibits the amount 
of income contributed from each article of capital as its 
source. The two methods, as applied to the example just 
given, are as follows : — 

Method of Balances 

Capital Income Outgo 

Income 

Logging camp $ 50,000 - . . . = + $50,000 

Sawmill 60,000 - $50,000 = + 10,000 

Lumber yard 70,000 - 60,000 = + 10,000 

Warehouse 80,000- 70,000 = + 10,000 

Stock of cloth in warehouse . . . 90,000 - 80,000 = + 10,000 

Stock of cloth of tailor .... 100,000 - 90,000 = + 10,000 

Stock of clothes of customers . . 110,000-100,000 = + 10,000 

$110,000 

Method of Couples 

Income Outgo 

iio^ooo^i^oorooa 

The two methods — balances and couples — show the 
same result, but from different points of view. By means 
of the method of balances we are enabled to see what part 
of the final net income is contributed by each of the articles 
in the group. By means of the method of couples, we are 
enabled to see of what the net income from the entire group 



158 NATURE OF CAPITAL AND INCOME [Chap. IX 

of articles consists; canceling by the oblique lines, we 
have left but one item, $110,000, representing the *' wear " 
of the suits. The two methods must not be confused. 
When we find by the method of couples that the net 
income of $110,000 consists exclusively of the use of 
suits of clothes, this does not imply that this net income 
is all due to the stock of clothes. To discover to what 
it is due, recourse must be had to the method of balances. 
We thereby see that only $10,000 of it is due to the stock 
of clothes, the remainder being due to the other capital 
instruments in the table and most of all ($50,000) to the 
logging camp. Combining the results of hoth methods, 
we may state that the total net income from the specified 
group of instruments consists of $110,000 worth of " wear " 
of suits and that this is due partly to the stock of clothes 
and partly to other capital. 

The two methods, that of balances and that of couples, 
correspond in a general way to the two methods for 
canceling liabilities and assets in capital accounts. The 
method of balances gave, it will be remembered, the 
amount of capital belonging to each individual ; the method 
of couples showed of what elements the total capital con- 
sisted. 

§9 

We have now followed the cancellations to which inter- 
actions lead, whether they be interactions of exchange or 
production. The case of exchange, however, needs further 
consideration. Since every exchange consists of two trans- 
fers, and every transfer of two items, a credit and a debit, 
the exchange evidently consists of four items in all, two 
of which are credits and two, debits. These four may be 
paired off in two ways, only one of which has thus far 
been mentioned. They stand, as it were, at the four 
corners of a square, as in the following scheme, which 
shows the credits and debits involved when goods worth $2 



Sec. 9] INCOME SUMMATION 159 

are sold. Tlie dealer credits his stock of goods and debits 
his "cash," while the buyer does the opposite. 







Stock of Goods 


Stock of Cash 


Seller 


+ $2 


-%2 


Buyer 


-S2 


+ $2 





The two transfers into which any exchange may be 
resolved are represented by the two columns of the table. 
But an exchange may also be resolved into two pairs of 
items represented by the two lines of the table. The 
items in the same horizontal line record the part taken in 
the exchange by one of the two exchangers. This pair of 
items constitutes his transaction, while the remaining pair 
constitutes, in like manner, the transaction of the other 
party to the exchange. The term " transaction," though 
somewhat vague in ordinary use, appears well suited to 
express the share in an exchange of one of the two who 
participate in it. 

Every exchange, then, consists of four items, and may 
be resolved either into two transfers (one for each prop- 
erty exchanged) or into two transactions (one for each 
exchanger). The first resolution has been considered; 
we proceed now to the second, and enter the subject of 
" double-entry bookkeeping." 

By double entry is meant the record of every double- 
faced event pertaining to a particular person, whether it 
be a transaction of that person with another or an in- 
teraction between the various categories of capital within 
his own possession. Double-entry book-keeping is most 
perfectly illustrated in the case of a fictitious person. 
The following account represents the entries during a 
given year for a dry goods company. In this account we 
observe that every item on the income side is balanced 



160 



NATURE OF CAPITAL AND INCOME [Chap. IX 



by an equal and opposite item on the outgo side. All 
items thus paired are represented by the same letters, the 
capitals being used for positive items and the small letters 
for negative. 



Income and Outgo of Dry Goods Company, for 
Year 1906 



Capital Source 


Income 


Outgo 






To goods 






bought . $5,000 c 


Stock of Goods 


By goods sold. $10,000 A 


To work of 

selling . 1,500^ 
To storage . 1,000(7 




By cash taken out 






for: — 






rent . . . $1,200 J5 






purchases . . 5,000 C 


To cash re- 


Cash 


wages . . . 1,600 Z) 


c e i V e d 




interest pay- 


from sales $ 10,000 o 




ment . . . 800^ 






profits . . . 2,000 i?' 




Store Lease 


By storage service $1,000 G 


To rent paid $1,200 6 


Rights to and 


By clerk work . $1,500 H 


To clerk hire $1,600 d 


obligations 






from employees 






Bonded debt 




To interest 
paid . . $800 e 


Capital stock 




To profits 
paid . . $2,000/ 



Let us consider the first item of capital, the stock of 
goods. This yields to the company as its gross income 
the money obtained from sales, amounting to $10,000 (A). 
The payment of this money into the cash drawer becomes a 
debit item (a) on the part of the stock of cash. Reversely, 
when the rent is paid the lease of the store is debited with 
S1200 (6), and the stock of cash which yields this value of 



Sec. 9] INCOME SUMMATION 161 

income is credited (B). In like manner all the transactions 
involving a payment or receipt of cash are entered on one 
side with respect to the cash, and on the opposite side with 
respect to some other capital som"ce. The category of the 
capital source called " rights to and obligations from 
employees " yields a certain amount of clerical work and 
other services appraised at $1500. This item credited {H) 
to the above-named source is here debited (h) to the stock 
of goods, to sell which requires the services of these 
employees. It may be that it should be debited to 
the store which they clean, or to some other article of 
capital on which they do work; but in any case it must 
be debited imder some head or heads. 

It will be seen that among the other items of capital 
which are sources of income or outgo are the bonds and 
stocks of the company. The bonds absorb $800 of in- 
terest, and the capital-stock, which is a residual claim on 
the company, absorbs any surplus of cash which it is 
decided to distribute in dividends. 

The two sides of the account of such a fictitious person 
necessarily balance. It cannot be otherwise, even if the 
company accumulates its profit instead of paying it to 
the shareholders; for, as has been seen, the money thus 
received is debited to the cash account. 

In practical accounting, the items would usually be sim- 
plified somewhat. It would not ordinarily be worth while 
to make an appraisement of the value of the use of the ware- 
house for storage as distinct from the storage charge, nor of 
the value of the work performed by the employees as distinct 
from the wages paid them. In the above accounts we have 
purposely distinguished these magnitudes, estimating the 
storage benefit as $1000 though the rent paid for it is $1200, 
and estimating the work done by employees as worth $1500 
though their wages were $1600. If, instead, we estimate 
the storage benefit at the rent figure and the employees' 
work at the wages figure, our accounts would contain four 



162 NATURE OP CAPITAL AND INCOME [Chap. IX 

items of $1200 and four of $1600. Of these, two of each 
might well be, and in practice usually are, dispensed with. 
These are the pair of items "storage service" ((? and g) 
and the pair "clerk work" {H and h). Omitting these, 
which are both appraised items, there will be left only 
cash transactions. These may be further simplified by 
dispensing with the two categories called " store lease " 
and "rights to and obligations from employees," by placing 
the rent (6) and the wages (d) under the head of " stock of 
goods." In other words, we charge the expenses for rent 
and wages directly against the goods stored and cared for 
instead of, as ui the table, charging against them " storage 
service" and "work of selling." There is no difficulty in 
recognizing the resulting accounts as those employed in 
ordinary bookkeeping. Occasionally the more elaborate 
accounting is necessary, as when a very old lease, hke some 
still in force in London, requires only a nominal rent charge 
compared with the benefits conferred. 

§10 

In the case of real persons, however, the two sides do not 
balance, for the accounts do not consist solely of double 
entries. To show this, let us recur to the accounts of the 
lawyer considered in Chapter VIII. The table on the 
opposite page reproduces those accounts, with some of the 
items given in greater detail. 

In these accounts, as in the previous ones, we have in- 
dicated the like items on opposite sides by like letters, the 
positive being represented by capitals and the negative 
by small letters. We observe that, as in the corporation 
accounts, many of the items will " pair." But, unUke the 
corporation accounts, the present accounts contain a resi- 
due of items which will not pair. The letters representing 
these unpaired items are designated by being inclosed in 
square brackets. They show that [B], [C], [D], [0] — the 
shelter of the house, use of furniture, use of food, use of 



Sec. 10] 



INCOME SUMMATION 



163 



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164 ^ NATURE OF CAPITAL AND INCOME [Chap, IX 

clothes, jewelry, etc. — constitute a kind of income which 
does not appear elsewhere as outgo. 

§11 

We found, when studying the accounts of instruments, the 
chain of productive services of the lumber camp, etc., that 
there always remains some outer fringe of uncanceled in- 
come produced by the capitalistic machine. We have now 
reached this same kind of outer fringe in studying the 
accounts of persons, provided they are real persons. This 
outer fringe consists of what economists have usually called 
" consumption." All other services are merely preparatory 
to such services, and pass themselves on from one category 
of capital to another. Thus the income from investments, 
being deposited in bank, is outgo with respect to the bank 
account; the bank account yields income by paying for 
stocks and bonds, food, etc., but in each case the same 
item enters as outgo with respect to these or other cate- 
gories of capital. In all these cases the individual receives 
no income which is not at the same time outgo. It is 
only as he consumes the food, wears the clothes, or uses 
the furniture that he receives income. 

The question still remains whether the fringe we have 
reached is the final outer fringe, or whether we must not 
proceed one step further and regard the final services just 
mentioned as merely interactions between a man's external 
wealth and his own body. This question will be discussed 
in the following chapter. We are content here to leave the 
chains of services at the point where they reach the person 
of the recipient. 



CHAPTER X 

PSYCHIC INCOME 
§1 

The stage at which, in the previous chapter, we left in- 
come may be called the stage of final objective services. 
In other words, it is the stage at which the wealth of the ob- 
jective world at last acts upon the person of the recipient of 
income. This final income is that for which the economist 
is usually in search, and is that which the ordinary statistics 
of workingmen's budgets represent. It is clear from what 
has been said, that in this fiinal net income all interactions 
between articles of external wealth drop out, — all the 
transformations of production, such as the operations of 
mining, agriculture, and industry, all the operations of 
transportation, and all business transactions or exchanges. 
For, in all such cases, the debits and credits inevitably 
occur in pairs of equal and opposite items. The only 
items which survive are the final personal uses of wealth, 
ordinarily called "consumption." Let us rather call them 
enjoyable objective services. The main sorts of enjoyable 
objective services are the ' following : services of nourish- 
ment, services of housing and warming, services of clothing 
and personal adornment, services of personal attendance, 
services of amusement, instruction, and recreation, serv- 
ices of gratification of vanity. 

§2 

It is usually recognized by economists that we must not 
stop at the stage of this objective income.^ There is one 
more step before the process is complete. Indeed, no 

^ See Fetter's Principles of Economics, New York, 1904, Chap. VI. 

165 



166 NATUEE OF CAPITAL AND INCOME [Chap. X 

objective services are of significance to man except as they 
are preparatory to subjective satisfactions. 

The final subjective services come through the human 
body. No agent outside the body can yield them. All 
that persons or things outside of man can do is to stimulate 
his bodily organism. Even what are called services of amuse- 
ment or instruction cannot directly amuse or instruct the 
mind; they can only affect the body. An instructive 
book, for instance, renders its service simply and solely by 
reflecting light into the eye of the reader. It is necessary 
that these stimuU on the optic nerve should be transmitted 
through the nervous system before any mental instruction 
takes place. So a piano can of itself produce no sensations 
of tone. It merely produces external vibrations, which, 
through the ear and auditory nerve, ultimately result in 
sensation. All sound, sight, taste, smell, touch, come 
about through reactions of the nervous system to external 
stimuli. A man who receives a Turkish bath has received 
enjoyable income in the objective sense, but all the serv- 
ices of the water, towels, attendants, and other cooperat- 
ing agencies, while credited to them, must, if we treat man 
himself as capital, be regarded as debited to him. They 
result simply in cleaning and stimulating his skin. They 
are income from outside agencies absorbed by his body in 
order that he may later experience pleasant sensations or 
avoid unpleasant ones, through the enjoyment of health. 
Similarly the use of clothing and shelter prevents the 
occurrence of the sensation of cold, but their immediate 
objective service is simply in hindering the dissipation of 
heat from the body. They are disservices with reference to 
the body, just as similar care and protection of a horse are 
disservices with reference to it. 

When medicine is taken, it may, from the objective stand- 
point, be counted as a part of income, just as food, clothing, 
and other ordinary items. But it is clear that the services 
of medicine are (or are supposed to be) the repairing of the 



Sec. 3] PSYCHIC INCOME 167 

body, and, although credited to the medicine, should be 
debited to the body, just as the services of a carpenter are 
credited to him but debited to the house which he mends. 
So the services of a dentist, far from producing any immedi- 
ate satisfactions, have for the moment quite an opposite 
effect, but result later in better service of one's own teeth. 
They are credited to the dentist, but debited to the body. 
The "consumption," or use of food, though it is a service of 
the food, is a disservice of the body ; for food stands in the 
same relation to the body as fuel to a furnace or repairs to 
a house. The final income consists of the subjective sat- 
isfaction of appetite and the other satisfactions which 
the intake of food enables the body to yield to the mind. 
These include not simply the immediate gratification of the 
palate, but the promotion of pleasant sensations or the 
avoidance of unpleasant ones later on. In other words, 
the consumption of food, by preserving health and main- 
taining life, enables the body to yield better and longer- 
continued income to the mind in future years, just as the 
repairs on a house enable it to yield shelter a long time after 
the repairs are made. 

§3 

These and other illustrations will show that, if we in- 
clude the body as a transforming instrument, while we 
must credit with their respective services all these outside 
agencies, such as food, clothing, dwelHng, furniture, orna- 
ments, and other articles which, as it were, bombard a 
man's sensory system, we must also at the same time debit 
the body with these same items. In this case the only sur- 
viving credit items after these equal debits and credits are 
canceled are the resulting final satisfactions in the human 
mind. In other words, in order that the external world 
should become effective to man, the human body must be 
considered as the last transforming instrument. Just as 
there is a gradual transformation of services through the 



168 NATURE OF CAPITAL AND INCOME [Chap. X 

farm, flour mill, and bakery, so is there a final transforma- 
tion within the human body itself. It is a sort of factory, 
the products of which are the only final uncanceled income 
of the consumer. In a complete view of productive pro- 
cesses, the human machine is no more to be left out of con- 
sideration than machines which handle the wheat in its 
prior stages. 

All objective income, therefore, is entirely erased or 
negatived as soon as we apply our accounting to the body 
of the recipient. The services of which that income consists 
empty out, as it were, their quota into the human body, but 
the ultimate result is not finally received until it emerges 
in the stream of consciousness. 

We define subjective income, then, as the stream of con- 
sciousness of any human being. All his conscious life, 
from his birth to his death, constitutes his subjective in- 
come. Sensations, thoughts, feelings, voHtions, and all 
psychical events, in fact, are a part of this income stream. 
All these conscious experiences which are desirable are posi- 
tive items of income, or services ; all which are undesirable 
are negative items, or disservices. We have avoided ex- 
pressly the statement that subjective income consists of 
pleasure, or of pleasure minus pain. These terms have been 
too loosely used by economists, and such use has involved 
them in unnecessary controversy with psychologists. It is 
better to avoid such disputes, and content ourselves with 
the simple statement that subjective events which are de- 
sirable are services, and those which are undesirable are 
disservices. This statement conforms to the definition of 
services and disservices originally given, and does not com- 
mit us to any psychological theory of pleasure or pain. 
Some psychologists would maintain that pain, to an ascetic, 
may be just as much an object of desire as pleasure.^ 

1 For instance, of the founder of the Sacred Heart Order, we read 
that, — 

"Her love of pain and suffering was insatiable. . . • 'Nothing 



Sec. 4] PSYCHIC INCOME 169 

Nor is it necessary to take sides in the controversies re- 
garding the relations between mind and body. We are 
not concerned with cause and effect, but with means and 
end, and, whatever may be the causation of mental states, 
the human body is certainly the means by which the good 
from external wealth is finally communicated to the con- 
sciousness of the owner. 

§4 

The two kinds of final income, the physical and the 
psychical, or the objective and subjective, are both legiti- 
mate in their proper spheres. Usually the physical and 
psychical income are equal to each other in value. A loaf 
of bread which yields ten cents' worth of services presumably 
gives ten cents' worth of immediate satisfaction. When one 
enjoys a musical concert worth one dollar, it does not matter 
whether we say that the services of the musicians in pro- 
ducing vibrations are worth one dollar, or the enjoyment 
which these vibrations occasion in the mind is worth this 
sum. When rent is paid for a house, this is generally 
taken to measure also the subjective comfort obtained 
through it. 

Nevertheless, there are several points at which the valua- 
tions of subjective and objective income are different, and 
three of these are sufficiently important to emphasize. 

The first case is that in which the transformation within 
the body takes a long time. Here the two species of in- 
come do not correspond. For instance, the instruction 
received by an apprentice in preparation for his trade is a 
service rendered to him in the training of his body in manual 
dexterity, in order that, a few years later, this manual 
dexterity may increase his income-earning power. Ap- 

but pain,' she continually said in her letters, 'makes my life support- 
able.' " Bougand, Hist, de la bienheureuse Marguerite Marie, Paris, 
1894, pp. 171, 265. Cf. also pp. 386, 387. Quoted from William 
James, Varieties of Religious Experience, 1902, p. 310. 



170 NATURE OF CAPITAL AND INCOME [Chap. X 

prenticeship is, as it were, an investment in the body, to be 
returned at a later time (with interest), just as the plant- 
ing of a tree is an investment in the tree in order that its 
fruit may be secured in later years. At the time of tree 
planting there is no net income, for the work credited the 
tree planter is debited the tree; it is only when in after 
years the tree bears fruit or other product that any return 
is obtained from the planting. Similarly, the work of 
teaching the apprentice should be credited to the teacher 
and debited to the apprentice's body ; the final satisfactions 
will not come until the acquired knowledge becomes 
effective. All this can be faithfully recorded only in the 
complete accounting which includes subjective income. 

The same principles apply to any training or education 
for a profession. When a young man studies law, medi- 
cine, journalism, music, or prepares for any other profes- 
sion, he is investing in his own person, with the hope that 
the sums thus invested may ultimately be returned to him 
(with interest). The same is true of physical training. 
Many of the most successful men are those who, Uke 
President Roosevelt, in early life saw the wisdom of 
developing a strong body, and in consequence have in- 
creased their productive power in mature years. 

§5 

The second point at which subjective and objective 
income diverges is found in occupations whose special grati- 
fication or irksomeness renders their return in psychical in- 
come widely different from their return in objective income. 
This is frequent in conditions of labor. Properly speaking, 
objective income takes no account of the toil of the laborer. 
The workingman who earns $2 a day earns double the ob- 
jective income of one who earns SI a day. Yet if the work 
of the former is difficult, loathsome, or dangerous, it may 
well be that many would prefer the nominally smaller in- 
come rather than endure these disadvantages. These facts 



Sec. 5] PSYCHIC INCOME 171 

have often puzzled economists, and the question has been 
asked whether any allowance should be made for disagree- 
able trades, such as that of the hangman, and whether it is 
fair to say that a workingman who earns $500 a year by 
the sweat of his brow really gets as much as a capitalist 
who receives an effortless $500 from stocks and bonds. 
The answer to these questions is now evident. So far as 
objective income is concerned, no allowance should be 
made. That is, the returns to the laborer are all to be 
counted gross and not net, no deduction being made on 
account of so-called "mental anguish" or painful feelings. 
Objective income stops at the threshold of the laborer's 
body. It does not follow beyond this point and include 
what the body communicates to the mind.^ 

But, by passing to subjective income, we avoid some of 
the manifest unfairness in the usual statistical comparisons 
which contrast a capitalist's income with that of a laborer, 
or contrast with each other the incomes of various labor- 
ers, some of whose tasks are difficult and others easy. To 
obtain one's net income we must subtract from the sub- 
jective satisfactions the subjective efforts of attainment. 
A laborer who receives $2 a day may work so hard for it 
as to justify a deduction of $1,50 for the effort, whereas 
the laborer who receives $1 a day may possibly need to 
deduct only 25 cents. The nominally $2 man would then 
be receiving a net income of only 50 cents a day, whereas 
the nominally $1 man would be receiving one worth 75 

^ The only way in which a man's person contributes to such objec- 
tive income is, as has been imphed in our illustrative accounts, through 
the work he performs upon external objects, in order that these may, in 
turn, yield back service to him. Objective income thus includes all 
the results of his own bodily exertions so far as they come to him via 
these outside agencies. A farmer, for instance, sows wheat, which 
is sold and yields him income. The farmer's services here start a 
circuitous process which is transmitted through the farm, the crops, 
the wheat, the proceeds from selling the wheat, the enjoyable com- 
modities purchased with these proceeds, and finally his own person 
again, to which those commodities minister. 



172 NATURE OF CAPITAL AND INCOME [Chap. X 

cents. Again, in the comparison between the capitalist's 
and laborer's income, we ought to say that the laborer 
who receives $500 a year, with an expenditure of effort 
appraised at $250, is only receiving one half as great an 
income as the capitalist who obtains, during the same 
period, dividends and interest to the extent of $500, with 
no effort whatever. 

It may be asked how an appraisement of labor is possible. 
From a practical or statistical standpoint the appraisement 
is difficult, if not impossible. Yet certain data are obtain- 
able. A servant applying for work asks not simply in 
regard to the wages, but in regard to the difficulty of the 
work, and will consent to do extra or disagreeable tasks only 
on condition of a definite increase in wages. In this case 
we may say that the increase in wages which is necessary 
to procure the consent of the laborer represents subjectively, 
to him or her, the increased difficulty of the work. In like ■ 
manner, a government employee who has at any time the 
option of retiring on half-pay may, at the point when he de- 
cides to retire, be said to regard the difficulty of his work 
as equal in his estimation to half of the income he receives 
for it. 

In general we may say that the proper method of apprais- 
ing the disagreeable element involved in one's work is to de- 
duct from the gross income that sum which the worker would 
be willing to sacrifice were it possible for him so to avoid the 
disagreeable element. That is, he is supposed to imagine 
an alternative condition, considered as an equivalent in his 
mind to the actual conditions under which he works, but 
which differs from them in two particulars : in being free 
from the labor or pain of toil ; and being deprived of a cer- 
tain amount of its earnings or rewards. If, for instance, 
the laborer who obtains $2 a day for eight hours' work 
estimates that this would be to him the equivalent of $1.50 
without labor, he has virtually made a deduction of 50 
cents a day for the irksomeness of his work. 



Sec. 6] PSYCHIC INCOME 173 

§6 

We have reached a convenient place in which to empha- 
size a point of great importance, but one which is seldom 
understood. This is, that most of what is called "cost of 
production" is, in the last analysis, not cost at all. We 
have found, in using the method of couples, that every 
objective item of cost is also an item of income, and that in 
the final total, no objective items of outgo survive cancellation. 
This principle holds true whether we stop our accounts at 
the bodily threshold, confining them to a record of ob- 
jective income, or extend them to include the body, thus 
yielding a record of psychic income. Those who have 
been accustomed to construct their theories of political 
economy on the assumption that "cost of production" is 
an essential and ultimate item, may do well to reflect care- 
fully on this proposition. It means that in a comprehen- 
sive view of production there is no cost of production in its 
objective sense at all. All of what is ordinarily called cost 
is really cost only with respect to certain accounts; it is 
always also income with respect to other accounts. This 
is true, for instance, of the cost of raw materials. It costs 
flour to produce bread ; but all that the flour costs to the 
baker is income to the miller. The same is true of wages. 
The employer counts his pay roll as cost of production, 
but the laborer counts it as earnings. 

Glimpses of the fact that all objective costs are always also 
objective income, and therefore disappear in the final sum- 
mation, are occasionally found in the books, especially 
those on land and interest, although the points of view have 
been variable and uncertain. There have been long dis- 
cussions as to whether rent enters into cost of production. 
The question has by many been negatively answered.^ 
Bohm-Bawerk has also maintained that interest was not 

^ See the interesting remarks of Jevons in the preface to his Theory 
of Political Economy, 3d ed., 1888, p. xlvii. 



174 



NATUEE OF CAPITAL AND INCOME 



[Chap, X 



an element in the cost of production. From what has 
been said it is evident that every rent and interest pay- 
ment, while it is a cost to the payer, is income to the payee. 
The total objective income of society consists wholly of 
positive items, such as the use of food and furniture, the 
shelter from houses, and the other direct services of wealth. 
There are no negative items in the account of social income 
which survive in the form of "costs of production." 

When we turn, however, to subjective income, we find the 
case somewhat different. Including the human organism 
as capital acted upon by the outer world and itself acting 
upon the inner world of consciousness, we not only carry 
the uncanceled fringe of services one step further and 
obtain as net income the subjective satisfactions from the 
use of food, clothing, furniture, dwelling, etc., but we find it 
necessary to include also the subjective efforts put forth by 
human beings in order that these satisfactions may accrue. 

Thus, to revert to the income account of the lawyer. We 
found that his net income consisted of the use of house $100, 
use of furniture $50, use of food $150, and other uses $2500, 
making a total of $2800. But if we include the lawyer's 
own person in our accounts, we should have to enter, in 
addition to all the previous items of income, the 
following : — 



Capital 
Source 


Income 
Satisfactions from 




Outgo 






shelter .... 


100 [P] 


Shelter . . . . 


1006 




Satisfactions from 








Self- 


use of furniture 


50 [Q] 


Use of furniture 


50 c 


Satisfactions from 










use of food . . 


150 [R] 


Consumption of 






Satisfactions from 




food .... 


. 150 d 




other uses . . 


2500 [S] 


Other uses . . 
Labor sacrifice . 


. 2500 
. 500 [t] 



Some of these additional items are subjective and some 
objective; the former are distinguished by italics. It is 
evident that the objective items, here debited to the person 



Sec. 7] PSYCHIC INCOME 175 

of the recipient, have all equal and opposite counterparts 
in the accounts as given in Chapter IX, §10. These 
same items were there entered as credits and constituted 
the "uncanceled fringe" of final objective income. They 
were designated as [B], [C], [D], [0]. Now, however, 
after the introduction of the new items, they cancel with 
the debits of like letters, h, c, 'd, o ; but another uncanceled 
fringe appears, namely, [P], [Q], [R], [S], which items are 
wholly subjective. These we have, for convenience, entered 
at the same figures as their objective prototypes. Their 
sum is therefore also $2800. But there also appears a sub- 
jective labor cost, [t], of $500 to express the personal labor 
and pain of the lawyer in his work. The result is that 
his net subjective income is not equal to the objective in- 
come of $2800, but is only $2300. 

When we have reached this final stage in our inquiries, 
therefore, we find the only ultimate item of cost to be labor 
cost, or, if the term "labor" be not itself suflaciently 
broad, labor, anxiety, trouble, annoyance, and all the other 
subjective experiences of an undesirable nature which are 
necessary in order that the experiences of an agreeable na- 
ture may be secured.^ In a sense, therefore, the socialists 
are quite right when they say that labor is the only true cost 
of production, although some of the conclusions which they 
deduce from this proposition are not justifiable. 

§7 

The third discrepancy between subjective and objective 
income is due to the fact that certain agreeable and dis- 
agreeable experiences are due directly to the character of 

1 It may be well here to emphasize the distinction between work 
and labor which has been so well drawn by Professor J. B. Clark. 
The work performed consists of the services rendered, and is posi- 
tive; the labor consists of the efforts of performing those services 
and is negative. The work is objective; the labor is subjective. 
Properly speaking, an employer does not pay a man for his labor, 
but for his work. 



176 NATURE OF CAPITAL AND INCOME [Chap. X 

the body itself. A large part of our subjective income is 
due to our condition of health or disease. A man with a 
good constitution has a more agreeable stream of con- 
sciousness, or subjective income, than one without. The 
pains and sufferings of illness here find a place in the com- 
plete accounts of income and outgo. It is evident that 
the wealthy man who confessed that he would exchange all 
his millions for a young and vigorous body may be the 
recipient of a large objective income, but not enjoy as 
much subjective income as Walt Whitman, who had 
scarcely a dollar in the world. 

That these subjective items are by no means to be de- 
spised by the economist, who has far too long busied himself 
with a study of the superficial objective phenomena, is evi- 
dent when we consider that a healthy body is absolutely 
essential for receiving and enjoying the income from external 
wealth. The man who is short-sighted enough to lose his 
health in the pursuit of what he calls wealth will soon be 
spending all of this sort of wealth to regain health ; and we 
need only visit the health resorts of Colorado and Cahfornia 
to be struck with the number of cases of business men who 
have found themselves in this predicament. Economists, 
by fixing attention exclusively on physical phenomena, 
leave out of account the most essential element of all, the 
vigor of human fife. The true "wealth of nations" is the 
health of its individuals. A nation consisting of weak, 
sickly, and short-hved individuals is poor compared with a 
nation whose inhabitants are of the opposite type. Hence 
it is that the devices of modern hygiene, sanitation, and 
preventive medicine, which tend to increase human work- 
ing power and enjoying power, are of greater economic 
import than many of the luxurious and enervating devices 
commonly connoted by ''wealth." 

We see, then, that subjective income means simply one's 
whole conscious fife. Every item of it comes via the body 
of the person. 



Sec. 8] PSYCHIC INCOME 177 

§8 

As to the measurement of the items entering into this 
psychic stream, the same principles apply which have 
already been laid down for the measurement of other mag- 
nitudes. First, all Hke events are measured by simple 
counting. Secondly, so far as it is possible, a valuation in 
terms of money is placed on them, as on objective services. 
To accomplish this appraisement it is only necessary for the 
individual to answer the question what money is he willing 
to pay for any enjoyment brought about by means of exter- 
nal wealth, such as a box of sweets or a cigar. If the event 
is one which cannot be connected with purchasable com- 
modities, it is necessary to imagine an exchange, even when 
actual exchange is impossible. 

We have now followed the method of couples from the 
balance sheet for a particular article of capital, or group 
of articles, to the entire capital goods of an individual or 
of society. The result has been inevitably to lead us to a 
consideration of the psychic stream of events as final in- 
come, all the agreeable items being on the credit side and 
the disagreeable ones on the debit side. But the methods 
which have been given also enable us to stop at any earher 
point. There are two such earlier points which are 
convenient and logical. The final objective income is one ; 
the other has its existence only in a highly developed 
civilization Uke the one now existing in western Europe 
and America, and consists of the familiar "money in- 
come" of an individual, that is, his money receipts from 
all capital sources, less his money outgo to them. The 
income of a person reckoned by these three methods will 
ordinarily be very similar, though in theory, and sometimes 
in practice, it may differ widely. As long as we under- 
stand the various kinds of income, and the relations be- 
tween them, we are at liberty to consider any one of them 
as "income" in its proper place. But we can scarcely 



178 NATURE OF CAPITAL AND INCOME [Chap. X 

understand any one without having had at least some 
view of both of the others. 

§9 

Having completed our survey of the summation of the 
elements of income, we may properly pause to classify these 
items. They fall naturally into three groups. The first 
group includes those items of income which are positive 
and not negative, that is, the agreeable experiences of sub- 
jective income, for these, as we have seen, are the only 
final uncanceled positive items. The second group in- 
cludes items which are negative but not positive, namely, 
disagreeable psychical experiences, and consists of two 
classes: (1) the labor and trouble which are sacrificed for 
the sake of procuring income through objective channels, 
in other words, the toil of the producer; and (2) the dis- 
agreeable impressions produced in one's consciousness by an 
abnormal state of the body, as aches, pains, and all sorts 
of illness, but which are not, like toil, voluntarily incurred 
for the sake of future return. The third group includes 
what we have called interactions, or items which are at 
once positive and negative, according to the point of view. 
Both of the first two groups are entirely subjective, and 
the last is entirely objective. The third group, interac- 
tions, constitutes by far the bulk of the items entering 
into income accounts, and includes all of those which 
enter into practical bookkeeping. It may be subdivided 
into two groups: (1) interactions outside of the human 
body, and (2) interactions between external wealth and 
the human body, or what have been called "final objec- 
tive services." The following scheme shows further sub- 
divisions : — 



Sec. 9] 



PSYCHIC INCOME 



179 



■ Pure services (subjective) 

f labor (cost of production) 
Pure disservices (subjective) | ^^^^ ^^^ ^^^^j. discomforts 



Services 



Interactions 



between objective wealth 

and body of owner 
(final objective services) 



nutrition 

clothing 

housing 

amusements 

instruction 

etc. 



, , . f agricultural 
r production | manufacturing 



between transportation 

objective \ 
articles 



commerce 



(advertising 
organizing 
indemnifying 
etc. 



PART III. Capital and Income 



Chapter XI. Foue Income-Capital Ratios 

Chapter XII. Concept of Eate of Interest 

Chapter XIII. Value op Capital 

Chapter XIV. Earnings and Income 

Chapter XV. Income and Capital Accounts 

Chapter XVI. The Risk Element 



CHAPTER XI 

FOUR INCOME-CAPITAL RATIOS 
§1 

We have now learned what capital and income are and 
how each is measured. We have seen that capital is not to 
be confined to any particular part or kind of wealth, but that 
it applies to any or all wealth existing at an instant of time, 
or to property-rights in that wealth, or to the values of that 
wealth or of those property-rights. We have seen that in- 
come is not restricted to money income, nor does it consist 
of a flow of commodities, nor is it a composite of commodities 
and services, nor is it necessarily regular in its receipt, nor 
must it necessarily be such as to leave capital unimpaired ; 
but that it consists simply of the services of wealth, and 
that, analogously to capital, income may be measured 
either by the mere quantity of the various services rendered, 
or by their value. We have seen that in the summation 
both of capital-value and of income-value there are two 
methods available for canceling positive and negative 
items called the "method of balances" and the "method 
of couples." By the method of balances the negative items 
in any individual account are deducted from the positive 
items in the same account, and the difference, or balance, 
shows the net capital (or income, as the case may be) with 
which that account deals, whether this be the net capital 
(or income) of a particular owner, or of a particular article 
or group of articles of capital. The method of couples, on 
the other hand, cancels items in pairs and is founded 
on the fact that, as to capital, every liabihty rela- 

183 



184 NATURE OF CAPITAL AND INCOME [Chap. XI 

tion has a credit as well as a debit side, and that, as to 
income, every interaction is at once a service and a dis- 
service. 

We observed that the method of couples, fully carried out, 
reveals respectively wherein capital and income ulti- 
mately consist. We have seen that such a summation, 
applied to capital, gradually obliterates all partial rights, 
such as stocks and bonds, and leaves as the final result the 
concrete capital wealth of a community; and that when 
the method of couples is applied to income accounts, the 
"interactions" involved disappear, leaving an uncanceled 
outer fringe of services and disservices. If the method is 
continued as far as possible in the world of objective serv- 
ices, it leaves simply the direct or final services of objec- 
tive wealth as they affect the human organism; while, 
if the method is pushed one step further, it leaves, as the 
final income stream, simply the pleasant and unpleasant 
experiences of human consciousness. We found as one 
result of our study that so-called cost of production has no 
existence as an element of the objective income stream, and 
that, therefore, the only costs of production which are not 
also elements of income are the subjective labor and trouble 
of those engaged in that production. 

We have seen that capital and income are in many re- 
spects analogous, and are strictly correlative ; that all capi- 
tal yields income and that all income flows from capital — at 
least when the term " capital " is used in its broader sense, 
which includes human beings. The old proposition of the 
economists, therefore, that capital is that wealth which 
yields income, is correct, although the idea that such a 
statement is restrictive, and applicable only to certain kinds 
of wealth, is incorrect. 

§2 

Since capital and income are so intimately related, it 
becomes necessary to examine in detail what their relations 
are. The chief relations between capital and income are 



Sec. 2] FOUR INCOME-CAPITAL RATIOS 185 

represented by four ratios. As we have seen, both capital 
and income may be measured either in quantity or value. 
It follows that the relation of income to the capital which 
bears it takes four different forms, according as the income 
and the capital are measured in one or the other of these 
two ways. These four forms of the income-to-capital 
ratio follow : — 

(1) The ratio of the quantity of services per unit of time 
to the quantity of capital which yields those services may 
be called the physical productivity of capital. Thus, if 10 
acres of land yield, in a certain year, 60 bushels of wheat, the 
ratio of income to the capital may be expressed as 6 bushels 
per acre per year. This is its physical productivity. In 
Uke manner, if 10 looms will weave 500 yards of cloth in a 
day, the ratio of services to the quantity of capital, or the 
physical productivity of the looms, is 50 yards per 
machine per day. 

(2) The ratio of the valv^ of the income from capital to 
the quantity of the capital may be called the value produc- 
tivity. Thus, if 10 acres of land yield a net return worth 
$200 a year, the value productivity is $20 per acre per 
year. This is what has ordinarily been called the rent of 
land. The same principles apply to the rent of a dwelling 
or of any other article of capital. Another example of 
value productivity is found in the wages of the laborer. 

(3) The ratio of the quantity of services rendered by 
capital to the valu^ of the capital may be called its phys- 
ical return. Thus, if $100 worth of capital applied to land 
in the form, say, of agricultural implements adds to the yield 
of the land one bushel, the physical return of this capital is 
Y^ of a bushel per year per dollar invested. Such a con- 
cept of physical return is familiar to students of classical 
economics under the head of "doses" of capital appHed to 
land. 

(4) The ratio of the valu£ of services to the valv£ of the 
capital yielding them may be called the value return. Thus, 



186 NATURE OF CAPITAL AND INCOME [Chap. XI 

if a house worth $10,000 yields in any given year a net rent 
of $1000, the value return is ten per cent per year. An 
important case of value return is evidently the rate of in- 
terest. 
Thus we have four ratios : — 

1- Quantity of services per unit of time,^ physical productivity. 

quantity of capital, 

2- Value of services per unit of time, ^ ^^^^^ productivity. 

quantity of capital, 

3. Quantity of services per unit of time, ^ physical return. 

value of capital, 

4. Value of services per unit of time, _ ^^^^^ return. 

value of capital, 

These four magnitudes must be carefully distinguished. 
They are, as mathematicians say, of different " dimensions." * 
This fact is suggested in the four following phrases, which 
may be taken as typical : — 

1. Bushels per acre per year. 

2. Dollars per acre per year. 

3. Bushels per dollar|per year. 

4. Dollars per dollar per year. 

§3 

The failure to keep these four magnitudes clearly dis- 
tinguished has already led to a great many confusions in 
economic science. The spurious distinction between rent as 
the income from "land" and interest as the income from 
"capital" is a case in point.^ From this confusion comes 
the notion that land differs from "capital" in that there is 
a margin of cultivation for the former and none for the 

^ For a mathematical statement, see Appendix to Chap. XI. 

^ The error is fully exposed in Cannan's "What is Capital?" Eco' 
nomic Journal, June, 1897, pp. 283-284, and in Fetter's "The Rela- 
tions between Rent and Interest," a paper presented before the 
American Economic Association, December, 1903. See also Hicks's 
Lectures on Economics, Cincinnati, 1901, p. 228, and the present 
writer's "R61e of Capital in Economic Theory," Economic Journal, 
December, 1897, p. 524, and "Precedents for Defining Capital," 
Quarterly Journal of Economics, May, 1904. 



Sec. 3] FOUR INCOME-CAPITAL RATIOS 187 

latter; and that, whereas different qualities of land bear 
different rents, representing the difference in advantage 
between a particular grade of land and no-rent land, all 
parts of capital bear the same rate of interest. These 
errors come from unconsciously regarding the land in 
terms of quantity and the so-called "capital" in terms of 
value; in other words, from considering the income from 
land in the sense of value productivity, but that from capi- 
tal in the very different sense of value return. If, in mak- 
ing our comparisons, we abide consistently by either one 
of these ratios, the imagined distinction between rent and 
interest and between land and capital will vanish. It is 
quite true that the value productivity of land differs with 
different grades of land; but it is equally true that the 
value productivity of machinery, or of any other element of 
capital, so varies. New, high-grade, and efficient machinery 
bears exactly the same relation to machinery which is out 
of date and inefficient that fertile land bears to sterile. 
Similarly, different persons have different degrees of pro- 
ductivity, some having high and others low earning power. 
It was on this basis, in fact, that Francis Walker applied 
the Ricardian theory of rent to the explanation of entre- 
preneur's profits. 

On the other hand, if we fix our attention on value return, 
we find it indeed true that the value return called the rate of 
interest on "capital" (however narrowly capital may be 
conceived) is uniform, but we find it equally true that the 
value return on land is also uniform ; for land which yields 
a high rent will have a correspondingly high value, and, in 
consequence, the ratio of the rental to the value will be 
exactly the same as for lower grades. 

Other examples of confusion might be cited. We find 
some of them in the cruder theories of interest. The 
"naive" productivity theory,^ for instance, confuses phys- 

^ See Bohm-Bawerk, Capital and Interest, English translation, 1888, 
pp. 120-141. 



^ 



188 NATUEE OF CAPITAL AND INCOME [Chap. XI 

ical productivity and value return, and attempts to deduce 
the rate of interest from mere physical productivity, which 
is impossible. 

§4 

In this book we are concerned chiefly with the fourth 
relation, value return, or the ratio of the value of income 
to the value of capital. 
{^ The fundamental principle which applies here is that the 
value of capital at any instant is derived from the value of 
the future income which that capital is expected to yield. 
The expected services may, of course, not be the actual 
services. In our ignorance of the future we fix our present , 
valuations on the basis of what we expect the future to be. /— 

The principle of present worth is of fundamental impor- 
tance in the theory of value and prices. It means that the 
value of any article of wealth or property is dependent alone 
on the future, not the past. The principle has been imper- 
fectly stated as follows: "The value of any article is not 
determined by its cost of production, but by its uses." 
But the costs of production are disservices, and these, if they 
be future, enter into value on precisely the same terms as 
uses or services. They are discounted as are services. 
For instance, the value of the Panama Canal to-day is 
dependent upon the future expected services, taken in con- 
nection with the expected cost of completion. If these 
future elements be given, the value of the canal will be the 
same whether past cost was large or small, or nothing at 
all. Of course, the future expected cost for completing the 
canal is less than if some of the work had not been done 
already, so that the greater the past cost has been, the less 
the future cost will be, and hence the greater the value of 
the canal at present. 

Thus normally the value of capital will vary with the 
past cost of production. Moreover, the experience of the 
past enables us to make a better estimate as to future cost. 



Sec. 4] FOUR INCOME-CAPITAL RATIOS 189 

But, however determined, it is the estimated future cost 
alone which enters into the calculation of present value. 
All of these principles are well illustrated in the case of 
the canal. After some $300,000,000 had been sunk in the 
enterprise, the proprietors were willing to sell out for only 
$40,000,000. To them, therefore, it was worth less than it 
had cost. The effect of the work already done on the canal 
was certainly to lessen the labors of the present possessors, 
but it also at the same time opened their eyes to the magni- 
tude of the task still before them; hence the reduction in 
value to correspond to the new forecast of the future. 

No one will dispute that the buyer of any article of capital 
will value it for its expected services to him, and that " at 
the margin" of his purchases, the price he will pay is the 
equivalent to him of those expected services, or, in other 
words, is their "present worth," their "discounted value " 
or "capitalized value." But some doubt may be felt re- 
garding the professional seller. As to him, he is simply a 
speculator as to the possible demand. He sells for what he 
can get, affixing whatever price he believes will, in the end, 
profit him most, sometimes making out of the transaction 
more than his costs of acquisition, sometimes less, usually, or 
normally, covering those costs plus interest on them for the 
time elapsing between their occurrence and the sale. 

The same principle applies all the way back in the pro- 
duction processes. The labor expended is staked (either by 
the laborer or entrepreneur) in anticipation of the prices 
which the buyers will be willing to pay. If these anticipated 
prices are not expected to cover the value of the labor and 
other costs plus the interest upon them, the result will be 
that the labor and other costs will not be expended. Hence 
by trial and error the labor and other costs will, imder nor- 
mal conditions, gradually be fitted to the prices. 

When prices find this normal level at which costs plus 
interest are covered, it is not because the past costs of pro- 
duction have determined prices in advance, but because 



190 NATURE OF CAPITAL AND INCOME [Chap, XI 

the sellers have been good speculators as to what prices 
would be. If they had foreseen that prices would not cover 
costs and interest on costs, they would have refrained from 
production entirely, while if they had foreseen the opposite 
condition, that of large profits, competition would have 
tended to reduce these profits to the usual dimensions. 

We see, then, that although prices bear a normal relation 
to past costs, this relation does not always hold true ; and 
that, whether it holds true or not, the costs do not prede- 
termine the prices except in the sense that the producers 
have skillfully adapted the stocks available now, and those 
to be available at succeeding points of time, to the expected 
demand for them. 

It is not our purpose in the present book, however, to 
emphasize these principles, for they belong properly to the 
theory of prices. We merely premise them in order to 
proceed to the study of the relation between capital-value 
and income-value, that is, of what we have called *' value- 
return." 



CHAPTER XII 

CONCEPT OF RATE OF INTEREST 
§1 

From the last chapter we obtained the concept of 
value-return. This may be explicitly defined as the ratio 
of the value of the income which flows from a specified 
capital during a specified interval of time, to the value of 
that capital at a specified point of time. Thus, if on Janu- 
ary 1, 1900, a capital is worth $10,000, and during the year 
1900 this capital jdelds an income worth $500, the value- 
return is five per cent per annum for that year. If the in- 
come is perpetual and flows at a uniform rate, the value- 
return is called the rate of interest realized on the capital. In 
other words, the rate of interest is, briefly stated, the ratio 
between income and capital. As business men say, the rate 
of interest is the " price of money," or the " price of capital." 
This very common usage is based on the thought that any 
capital simi is the equivalent of some annuity. The usage 
has been needlessly condemned by economists on the 
ground that a different meaning should be assigned to the 
expression "price of money," viz. its "purchasing power" 
over goods in general. But the objection is not well 
founded, for it is evident that "purchasing power" includes 
not only purchasing power over a stock of goods but also 
purchasing power over a flow of income. If $100 will buy 
a perpetual annuity of $6 a year in Japan, while in England 
it will buy one of only $3 a year, the purchasing power of 
capital over income is six per cent in Japan, and only half as 
much in England. A millionaire in the first country will be 
able to command an income of $60,000 without trenching on 

191 



192 NATURE OF CAPITAL AND INCOME [Chap. XII 

his capital, whereas in England he can get but $30,000, and 
will, therefore, be just half as wealthy in actual income. 

§2 

The rate of interest has many meanings, and since the 
concept is so vital to our study, we shall specify carefully, 
in the present chapter, what these various meanings are. 
The meaning implied in the previous section postulates the 
existence of a perpetual annuity, i.e. a uniform and per- 
petual flow of income. Although such an annuity does 
not actually exist, it is often convenient to employ it as 
a vehicle of thought. Suppose $10,000 to-day will secure 
a perpetual annuity of $400 per year payable annually, 
the first payment accruing one year from the day of pur- 
chase ; then the rate of interest is said to be four per cent 
per annum payable annually; that is, the rate of interest 
(when the interest is payable annually) is the ratio between 
the rate of flow of a perpetual annuity and its equivalent in 
present capital. 

In case the income accrues semi-annually the case is 
slightly different. Let $10,000 to-day yield a perpetual an- 
nuity of $400 a year in semi-annual payments of $200 each, 
the first payment being due six months from date. Then 
the rate of interest is said to be four per cent per annum 
payable semi-annually. 

That these four-per-cent rates are not equivalent to 
each other is well recognized in practice, and can be made 
evident in various ways. The holder of the semi-annual 
annuity has a slight advantage over the holder of the annual 
annuity, because he receives half of each year's income 
six months earlier. He may, in fact, convert his income 
of $200 twice a year into an income of $404 once a year ; 
for in six months, besides receiving his first installment of 
$200, he may receive $10,000, by selling his annuity. He 
may then reinvest the entire $10,200 on the original terms, 
4 per cent payable semi-annually, and hence obtain a per- 



Sec. 2] CONCEPT OF RATE OF INTEREST 193 

petual annuity of $408, in semi-annual installments of $204. 
In six months more, or one year from the original invest- 
ment, he may realize $204 of income and $10,200 of " prin- 
cipal," or $10,404 in all. Of this he may reinvest the 
original $10,000, retaining $404, From this point onward 
he may repeat the same annual cycles of sales and 
reinvestments, and, therefore, receive $404 net, payable 
once a year. He is, consequently, better off by $4 a year, 
than the holder of an annuity of $400 a year, payable 
annually. In other words, a rate of interest of 4 per cent 
per annum, if the income is payable semi-annually, is 
equivalent to a rate of interest of 4.04 per cent per 
annum, if the income is payable annually. 

The same reasoning may be applied when the income 
accrues at quarterly or any other intervals.^ 

By subdividing the time of payment indefinitely, we may 
pass from an income obtained in installments to a continu- 
ous flow of income. The idea of a uniform and perpetual 
stream of income is nearly realized in certain cases, as in the 
West, where water rights are sometimes bought in the form 
of a "miner's inch" — a perpetual flow through a square 
inch opening under a head of six inches. Let us suppose 
that the water is worth $100 a year. If the right to such 
a perpetual and uniform flow can be bought for $2000, the 
rate of interest is five per cent "reckoned contiauously." 

We thus reach the conclusion that there are various 
senses of the rate of interest, according to the frequency 
of pajmaent, namely, — 

The rate of interest per annum, income payable annually. 

The rate of interest per annum, income payable semi-annually. 

The rate of interest per annum, income payable quarterly. 

The rate of interest per annum, income payable at other intervals. 

The rate of interest per annum, income payable continuously. 

The last named, while it is the least familiar in practice, is in 
some respects the most natural, and lends itself the most 

^ See Appendix to Chap. XII, § 1. 



194 NATURE OF CAPITAL AND INCOME [Chap. XII 

readily to mathematical transformations. The first, on the 
other hand, is the most frequently used in practical 
computations. 

§3 

We have considered the rate of interest as the price of 
capital in terms of income. If we consider reciprocally 
the price of income in terms of capital, we shall have what 
is called the "rate of capitalization." It is measured in 
years, namely, the number of years during which there 
would flow an amount of income equal to the capital. Thus, 
if 125,000 will buy a perpetual annuity of $1000 a year, the 
rate of capitalization is " twenty-five years' purchase." The 
concept of '' years' purchase " is common in England as 
applied to land rents. It is evidently interconvertible with 
the rate of interest. A rate of interest of four per cent indi- 
cates a " years' purchase " or rate of capitalization of 
twenty-five years. A rate of interest of two per cent 
indicates a rate of capitalization of fifty years. The rate of 
capitalization has thus as many meanings as the rate of 
interest, according as the income is payable annually, 
semi-annually, quarterly, etc., or continuously. 

§4 

The concepts of interest which have been given depend 
upon the concept of a perpetual annuity. But they can be 
made to apply also to terminable annuities. Thus, $10,000 
may yield at four per cent an income of $400 a year for 
ten years, at the expiration of which time the $10,000, or 
the "original loan," is returned. In such a case the loan 
may evidently be regarded as a purchase and resale of a 
perpetual annuity. A perpetual annuity of $400 is, for the 
price of $10,000, diverted to the lender's benefit, and at the 
end of ten years is restored to the borrower for the same 
sum. 

We may regard in this light even short-time loans. Thus, 



Sec. 4] CONCEPT OF RATE OF INTEREST 195 

if a man borrows $100 to-day and agrees to pay it back with 
interest at 4% in one year, we may conceive of him as 
having sold a perpetual annuity of $4 a year for $100, and 
at the same time as having bound himself to buy it back for 
$100 at the end of one year. The combined result of these 
operations amounts to an exchange of $100 this year for 
$104 next year. It is possible to use such a simple exchange 
between this year's and next year's money, as the basis of 
an entirely new definition of the rate of interest, and one 
which is independent of the idea of an annuity. When 
$100 to-day is exchanged for $104 next year, the ratio of 
exchange between the two simis is j^^. This ratio is not, 
of course, itself the rate of interest; the rate of interest is 
the excess, or premium, of \^^, above unity. In other 
words, the rate of interest is the premium, or " agio," above 
par of this year's dollars in terms of next year's dollars. 

Such a concept of interest may be called the premium con- 
cept, whereas the concept hitherto employed, or the price of 
capital in terms of an annuity, may be called the price con- 
cept of the rate of interest. To say that the rate of interest 
in the price sense is four per cent means that the price of $100 
of capital is $4 of income per annum forever. To say that 
the rate of interest in the premium sense is four per cent 
means that the price of $100 of one year's goods is $104 of 
the next year's goods. 

The premium concept of the rate of interest has been so 
much emphasized, notably by Bohm-Bawerk, that it 
seems advisable to repeat briefly, with respect to it, the dis- 
tinctions as to annual, semi-annual, quarterly, etc., reckon- 
ing. Let us suppose that $100 to-day is worth $102 six 
months hence. The rate of interest in the premium sense 
is here 2 per cent for the six months' interval, and is said 
to be " 4 per cent per annimi payable or reckoned semi-an- 
nuallyy It will be evident, however, that this is a little 
higher rate than 4 per cent per annum reckoned annually. 
Let us suppose that at the end of six months, at which time 



196 NATURE OF CAPITAL AND INCOME [Chap. XII 

$102 is due, the debt is renewed for another six months at 
the same rate. It is evident that the $102 will then, by 
''compounding," amount to $102 x 1.02, or $104.04. The 
interest then, at the end of a year, instead of being $4, is 
$4.04, In other words, 4 per cent interest reckoned half- 
yearly is equivalent to 4.04 per cent reckoned yearly, as was 
also the case under the price concept of the rate of interest. 
In the same way we may consider quarterly or other inter- 
vals for compounding. At the limit, the interval for com- 
pounding may be reduced to an instant.^ 

We have then two methods of defining interest. In 
both of them the time element is prominent. Before pass- 
ing on we should here remark that the time element enters 
not only as referring to the times of payment but also to 
the time of contract. A rate of interest implies not only 
the two points of time between which the goods for 
exchange are available, but also the point at which the de- 
cision to exchange them is made. It would be quite pos- 
sible, for instance, to agree in the year 1900 to exchange 
$1000 in the year 1901 for a given sum or series of sums 
returnable at still later dates. In this case the rate of 
interest for this exchange appertains to the year 1900, 
although execution of the contract does not begin until a 
year later and is not concluded until later still. These 
conditions have often been overlooked in treating statis- 
tics of the rate of interest. 

§5 

We have defined the rate of interest both in the 
"price" and the "premium" sense. The question now 
arises whether these two concepts are interchangeable. 
Under certain conditions they are, and under others they 
are not. Cases in which the two are interchangeable are 
shown in the following propositions. 

^ For the mathematical relations involved, see Appendix to Chap. 
XII, § 2. 



Sec. 5] CONCEPT OF RATE OF INTEREST 197 

(1) If the rate of interest, in the sense of a premium on 
this year's goods in terms of next year's goods, is the same 
year after year forever, then the rate of interest considered 
as the price of capital in terms of a perpetual annuity will be 
equal to it. 

A numerical example will make this clear. We shall sup- 
pose that the rate of interest is four per cent in the premium 
sense, i.e. that $100 at any moment during the period under 
consideration will buy $104 to be paid one year later. We 
are to show that as a consequence $100 will necessarily buy 
an annuity of $4 a year forever. Let us suppose, then, the 
premium rate being 4 per cent, that $100 is spent for $104, 
to be repaid one year later. Of this $104, when it is 
received at the end of the year, the investor reinvests $100. 
By our hypothesis of an unchanged interest rate, this $100 
will bring, at the end of the second year, another $104, 
of which in turn $100 is reinvested ; and so on indefinitely. 
By continually reinvesting, he obtains for his original $100, 
$4 a year indefinitely and $100 deferred indefinitely. If 
the process is perpetual, the $100 is deferred to infinity, 
and has no present value. Hence the original $100 obtains 
simply a perpetual annuity of $4 a year, and the rate of in- 
terest in the price sense is therefore also 4 per cent, which 
was to have been proved.^ 

It is evident that this reasoning may all be put in general 
terms, and that it applies equally to interest reckoned 
semi-annually, quarterly, etc., and continuously. 

(2) Conversely, if a given rate of interest in the price 
sense holds good to-day, next year, two years later, and so 
on indefinitely, then the rate of interest in the premium 
sense will be equal to it. 

This also may be readily shown by an example. If $100 
will buy $4 a year forever, the first $4 being due one year 

^ An alternative proof consists in obtaining the present value of 
each successive item of income and adding the results. This process 
is exemplified in the next chapter in obtaining the capital-value of a 
perpetual annuity. . 



198 NATURE OF CAPITAL AND INCOME [Chap. XII 

hence, the buyer of such an annuity at the end of one year 
may, immediately upon the receipt of his first $4, sell out 
his rights. By hypothesis they will bring $100. Conse- 
quently, he receives $104 in all for his $100 a year ago. He 
has thus virtually exchanged $100 one year for $104 the 
year after. That is, the premium rate of interest for this 
year is also 4 per cent. 

We see, then, that if the rate of interest in either of the 
two senses — price or premium — remains constant, the 
rate in the other sense will also remain constant and equal 
to the former. 

It is clear that the same reasoning applies to interest 
reckoned for any period of time, — semi-annually, quar- 
terly, continuously. 

§6 

But if the rate of interest does not remain constant, its 
two senses of price and premium are no longer interchange- 
able. Thus, suppose that the rate is 4 per cent in the 
premium sense for the first year, but 3 per cent for the 
second year and for all succeeding years. This means that 
$100 to-day will buy $104 next year, and that $100 next year 
will buy $103 the year after. Then $100 to-day will evi- 
dently not buy $4 a year forever, nor $3, but an intermediate 
amount, approximately $3.03, so that the rate of interest in 
the price sense is 3.03 per cent.^ 

Again, suppose that the rate of interest in the price sense 
is 4 per cent this year, but 3 per cent next year. This 
means that $100 to-day will buy $4 a year forever, and 
that $100 next year will then buy $3 a year forever. 
Then $100 to-day will not buy $104 next year, nor $103, 
but $137^. That is, the rate of interest in the premium sense 
is 37^ per cent.^ Thus a very slight change in the price rate 
of interest implies a great change in the premium rate of in- 

1 See Appendix to Chap. XII, § 3. 

2 See Appendix to Chap. XII, § 4. 



Sec. 7] CONCEPT OF RATE OF INTEREST 199 

terest. This goes to explain why, in the actual market, the 
rate of interest for short-time loans fluctuates so much 
more widely than the rate of interest on long-time invest- 
ments. It is scarcely necessary to exhibit statistics to show 
this, though they are easily obtained by comparing the 
fluctuations in the rate of interest on short-term and long- 
term loans, in the United States or in England. 

We see, then, that the two concepts of interest rate, though 
definitely related,^ are not always interchangeable. 

§7 

There is yet another device for indicating the terms of 
time exchanges. Besides the rates of interest and their 
reciprocals, the ratios of capitalization, there is the rate of 
discount. We have seen that if $104 due one year hence 
win buy $100 of present goods, then \^^ is the rate of ex- 
change between the two times and exceeds unity or par by 
yf-g-, the rate of interest. The rate of exchange between the 
two times, when taken in the opposite direction, is \^^ and 
this is less than unity or par by -^^^. This deficiency, 
which amounts to 3.9 per cent, is called the rate of discount. 
The nimiber representing the rate of discount is always 
slightly less than that representing the corresponding rate 
of interest.^ The rate of discount is practically employed 
only for short-time loans, usually less than a year, in which 
cases it better serves the purposes of rapid computation. 



The present chapter may be briefly summarized as fol- 
lows : — 

First, the rate of interest is a special case of "value- 
return," and may be approached from either of two stand- 
points, according as we consider it the price of capital in 

^ See Appendix to Chap. XII, § 5. 

^ For further discussion of the rate of discount, see Appendix to 
Chap. XII, §§ 6, 7. 



200 



NATURE OF CAPITAL AND INCOME [Chap. XII 



terms of a perpetual annuity, or the premium on the price 
of this year's goods in terms of next year's goods. These 
two definitions of the rate of interest we have found to be 
interchangeable when either one of them is assumed to be 
invariable ; but when this condition is not fulfilled the two 
are not interchangeable. 

Secondly, not only does the rate of interest have the two 
distinct meanings which have been given, but each mean- 
ing is subject to various interpretations, according as the 
interest is payable or reckoned annually, semi-annually, 
quarterly, etc., or continuously. 

Thirdly, as alternatives to the rate of interest we may em- 
ploy the rate of discount and the rate of capitalization. 
Both of these magnitudes also apply either in the price sense 
or the premium sense. Furthermore, like the rate of in- 
terest, they apply somewhat differently according as the 
reckoning is annual, semi-annual, quarterly, etc., or con- 
tinuous. 

The following table illustrates the various magnitudes 
which have been considered:^ — 



Equivalent Rates of Interest, Discount, and Capitalization 





A 

Mate of 
Interest 


B 

Bate of 
discount 


C 

Reciprocal 

of A, or 

Bate of 

Capitalization 


D 

Beoipro- 
cal of B 


Reckoned annually . . 
Reckoned semi-annually 
Reckoned quarterly . . 
Reckoned continuously 


4.00% 
3.96% 
3.94% 
3.92% 


3.85% 
3.88% 
3.90% 
3.92% 


25.0 yrs. 

25.3 yrs. 

25.4 yrs. 
25.6 yrs. 


26.0 yrs. 
25.8 yrs. 
25.6 yrs. 
25.6 yrs. 



Since the sixteen magnitudes in this table may be taken 
either in the price or the premium sense, and since, when in- 

1 For their mathematical " dimensions," see Appendix to Chap. 
XII, § 8. 



Sec. 8] CONCEPT OF RATE OF INTEREST 201 

constancy enters, the two senses will involve two unequal 
magnitudes, we have here represented or implied thirty- 
two possible magnitudes. The means for expressing time 
exchanges between goods of the same kind thus present 
an embarrassing variety. But since it is easy to proceed 
from any one of them to all the others, it is evident that we 
need not, in general, employ more than one. The one 
which is practically the simplest, and which, therefore, we 
shall hereafter employ in this book is: the rate of interest 
per annum reckoned annually and considered as a premium 
on the goods of one year compared with those of the year follow- 
ing. 



CHAPTER XIII 

VALUE OF CAPITAL 



Having found what constitutes a rate of interest, we are 
now enabled to pursue our study of the relation between 
capital and income. We found in Chapter XI that these rela- 
tions are of four kinds, according to whether the income 
and the capital are measured in quantity or in value. The 
fourth of these, "value-return," brought us to the concept 
of a rate of interest. 

The rate of interest acts as a link between income-value 
and capital-value, and by means of this link it is possible 
to derive from any given income-value its capital-value, i.e. 
to "capitalize" income. 

To do this, we assume that the expected income is fore- 
known with certainty, and that the rate of interest (in the 
sense of an annual premium) is foreknown, and also that it 
is constant during successive years. With these provisos 
it is very simple to derive the capital-value of the income to 
be yielded by any article of wealth or item of property ; in 
other words, to derive the value of that wealth or prop- 
erty. That value is simply the present worth of the future 
income from the specified capital. This is true whether 
the income accrues continuously or discontinuously ; 
whether it is uniform or fluctuating; whether the install- 
ments of income are few or infinite in number. 

We begin by considering the simplest case, that, namely, 
in which the future income consists of a single item accru- 
ing at a definite instant of time. If, for instance, one holds 
a property right by virtue of which he will receive, at the end 

202 



Sec. 1] VALUE OF CAPITAL 203 

of one year, the sum of $104, the present value of this 
right, if the rate of interest is 4 per cent, will be $100. 
If the property is the right to $1 one year hence, its present 
value is evidently oi or $0,962, and if the sum to which the 
property entitles the owner is any other amount than $1, 
its present value is simply that amount divided by 1.04 
or multiplied by .962. Thus the present value of $432 
due in one year is ^, or 432 x .962, which is $416.^ 

If the future sum is due in two years, and the rate of 
interest is still 4 per cent, it is evident that $1 to-day is 
the present value of $1.04 next year, which in turn (by 
compounding) will then be the present value of $1.04 x 1.04 
(i. e. [1.04] 2, or $1,082) at the end of the second year. The 
$1,082 is called the "amount" of $1 at the end of two 
years, and $1.04 is the "amount" of $1 in one year. 

Similarly, in three years (1.04)^ is the "amount" or sum 
worth $1 in present value; and so on for any number of 
years. These results show what $1 to-day is worth at 
the end of any number of years. And conversely, from 
them it is easy to see what $1 due at the end of any number 
of years is worth to-day. We have already seen that the 
present worth of $1 due in one year is j^, or $0,962. 
Similarly, the present value of $1 due at the end of two, 
three, etc., years is respectively i^„ ^j;^, etc.^ Knowing 
the present value of $1, we may evidently find that of any 
other sum by simple proportion. 

To illustrate these results geometrically, let us represent 
time by horizontal lines, and the value of the capital by 
vertical Hues; then the curve A A' A" A'", as shown in 
Figure 1, will exhibit the relative values at any two in- 
stants, exchangeable on the basis of a given rate of interest, 
compounded annually. 

The point B represents the present instant; B', the in- 

1 For the general mathematical treatment, see Appendix to Chap. 
XIII, § 1. 

^ For a mathematical formulation, see Appendix to Chap. XIII, § 2. 



204 



NATURE OF CAPITAL AND INCOME [Chap. XIII 



stant a year hence; B" , that two years hence; B'" , three 
years hence; and B^^\ t years hence. AB represents any 
present value, A'5' the " amount ' ' of this sum one year hence, 
A"B" the ''amount" two years hence, etc. Consequently, 
AB also represents the present value of A'B' due one year 
hence, or of A"B" due two years hence, or of A'-'^B^'^ due 
t years hence. The curve AA(*) is an " exponential curve," 
this being the name given to a curve which ascends in geo- 



B' B" B"' 



m 



Fig. 1. 



metrical progression, i.e. ascends so that the successive 
vertical lines, AB, A'B', A"B", andA"'5'"(ordinates), 
taken at equal intervals, increase in length at a uniform 
ratio. We shall, however, for economic purposes, christen 
this curve the "discount curve." 



§2 

The principles which have been explained for obtaining 
the present value of a single future sum apply to many 
commercial transactions, especially to the valuation of bank 
assets, which exist largely in the form of "discount paper," 
or short-time loans of other kinds. The principles also 
apply, though in combination with those of risk and for- 
eign exchange, to that form of property called "bills of 



Sec. 2] VALUE OF CAPITAL 205 

exchange." Still another application is to wealth which is 
in course of trade and of which, therefore, the only service 
to the owner consists in its sale. It is on this principle 
that a dealer reckons the value of his stock, by discount- 
ing its selling price for the time which will probably elapse 
before it is sold — deducting, of course, the prospective 
expense of selling, discounted in like manner. Similarly, the 
value of any article of wealth reckoned when that wealth 
is in course of construction is the present value of what it 
will bring when completed, less the present value of the 
cost of completion. For instance, the maker of an auto- 
mobile will appraise it, at any of its stages in course of 
construction, as worth the discounted value of its probable 
return when subsequently finished and sold, less the dis- 
counted value of the costs of construction and selling 
which still remain. Of course, the element of risk cannot, 
in such cases, be overlooked ; but its consideration belongs 
to a later chapter. 

Another application of these principles of capitalization 
is to goods in transit. A cargo leaving Sydney for Liv- 
erpool is worth the discounted value of what it will fetch 
in Liverpool, less the discounted value of the cost of carry- 
ing it there. Other classical examples are wine, the value 
of which is the present worth of what it will be when 
"mellow" and ready for consumption; and young forests, 
which are worth the discounted value of the lumber they 
will ultimately form. In Germany and some other coun- 
tries, such appraisement of forests is now worked out with 
considerable precision. 

§3 

It seldom happens, however, that there is one item only of 
income or outgo earned by an article of capital. The items 
are unusually numerous. Perpetual annuities, for in- 
stance, form an important class, in which these items recur 
in equal amounts and during equal intervals forever. We 



206 NATURE OF CAPITAL AND INCOME [Chap. XIII 

have already seen, in the last chapter, that if a person owns 
the right to $1 a year payable at annual intervals forever, 
its present value, reckoned at four per cent, is ~, or $25. 
If his annuity is $2 per year, its present value is evidently 
double this, or $50 ; and if it is any other sum, its present 
value is found by multiplying in the same way. Thus, an 
annuity of $17 is worth jj. In other words, the value of a 
perpetual annuity is found by dividing the annual income 
by the rate of interest,^ or, what amounts to the same thing, 
by multiplying the income by the rate of capitalization, 
also called the number of years' purchase. This proposi- 
tion, however, serves to determine only that capital-value 
which an annuity possesses at its inception {i.e. one year 
before the first installment) or at any other point taken 
one year in advance of the first of the installments to be 
included in the calculation. The value of the annuity, 
taken immediately before any installment of income falls 
due, is evidently greater than the above, by the amount 
of that installment. Thus, if the rate of interest is four 
per cent, a perpetual annuity of $4 a year, of which the 
first payment falls due one year hence, is worth $100 to- 
day, and is also worth this same sum at any instant 
immediately following the payment of an installment. 
But next year, immediately before the first paj^ment 
becomes due, it will be worth $104. At any intermediate 
point between the present when it is worth $100 and a 
year hence when it is worth $104, it will be worth an 
intermediate amount, determined by the discount curve; 
for its value will always be the discounted value of the 
$104, which could be realized on it at the time of the next 
interest payment. As soon as this payment has passed by, 
the value will drop to $100 again, after which it will gradu- 
ally ascend as before, and so on, following a series of curves 
like the teeth of a saw, as shown in Figure 2. In this 
diagram, the value of the annuity is represented by suc- 
* For a mathematical statement, see Appendix to Chap. XIII, § 3. 



Sec. 3] 



VALUE OF CAPITAL 



207 



cessive vertical lines, four units in height, each representing 
$4, and situated one unit of time apart/ 

If the annuity is '^ deferred," i.e. does not begin till some 
future time, its present value is the discounted value of 



4 



J4 



Jl- 



J4 11. 



Fig. 2. 



that value it will possess when it does begin. Thus, in- 
terest being four per cent, while $100 is the value of a $4 
annuity beginning to-day (by which, as we have seen, is 
meant that its first installment falls due one year from 
to-day), the present value of an annuity deferred one year 
later will be only j^, or $96.15, and the present value of an 
annuity deferred five years is ■^^„ or $92.46. The value 
of the annuity at any time before its inception at the point 
A is shown by the height at any point of the discount 
curve through A. 

In the preceding discussion, the income, which is sup- 
posed to accrue in installments, is represented by separate 
successive vertical lines. But when the income is sup- 
posed to flow continuously, it becom.es necessary to repre- 
sent it by an area. In the "area" method, time is still 

^ For further discussion of the effect of reckoning interest for dif- 
ferent time-intervals, see Appendix to Chap. XIII, § 4. 



208 



NATURE OF CAPITAL AND INCOME [Chap. XIII 



represented by horizontal lines, and vertical lines or ordi- 
nates are employed — not to represent income, but rate of 
income. Thus, in Figure 3, AC is the rate of income flow- 
ing at the instant A, and BD is the rate at the instant B. 



Fig. 3. 

As a consequence, the income which flows through any 
period of time, AB, is represented by the area ABDC. It 
is therefore the time AB multiplied by the average rate. 
In the case of a uniform flow of income, CD reduces to a 
horizontal straight line. The area method will hereafter 
be used wherever continuous income is in question.^ 

§4 

Actual examples of true perpetual annuities cannot be 
said to exist ; but for practical purposes, some government 
"rentes" are perpetual annuities, also railway leases for 
999 years. While the capital value of a perpetual annuity 
of $4 a year, capitalized at 4 per cent, is $100, that of an 
annuity of $4 a year for 50 years is $85, for 75 years is $94, 
for 100 years $98, and for 200 years $99.96. It will be seen, 
therefore, that for any ordinary rate of interest, an annuity 
extending a century or more is practically equal in value to 
a perpetual annuity. 

Among non-monetary examples may be cited as per- 
petual annuities the before-mentioned water rights in the 
West. These are often sold by the miner's inch, i.e. a 
theoretically perpetual flow of 1^ cubic feet per minute, 

^ For a fuller statement of the area method, as related to the line 
method, see Appendix to Chap. XIII, § 5. 



Sec. 5] VALUE OF CAPITAL 209 

which is supposed to be the rate at which water will flow 
through an aperture of one square inch with a "head" 
of six inches. The "first" inches are often so sure to con- 
tinue as to be guaranteed. Again, if we overlook the 
element of risk, the S^ hares in joint stock companies 
often exemplify perpetual annuities. 

Turning from capital proper y to capital wealth, we find 
in land an approximate example of capital yielding a per- 
petual annuity. Land is often capitaUzed on the basis of a 
perpetual and uniform income, in the form of crops or other 
uses. It is then valued at a certain number of years' pur- 
chase. These so-called " natural and indestructible powers 
of the soil," however, which such a calculation assumes, do 
not always exist, and when they do exist, do not always 
yield a perpetual annuity. Mines and quarries become 
exhausted, while much land yields an irregular, increasing, 
or decreasing income stream. 



We turn now from perpetual to terminable annuities. 
Suppose that a man possesses a ten-year annuity of $100 a 
year. This means that he has the right to receive ten annual 
payments of $100 each, the first falling due one year from 
the present moment. It is clear that such an annuity differs 
from a perpetual one by lacking the infinite succession of 
payments after the ten years are past. In short, the 
terminable annuity is simply a perpetual annuity dated 
to-day, less a perpetual annuity deferred ten years. There- 
fore, the present value of the terminable annuity is simply 
the difference between the present value of the two perpet- 
ual annuities. Of these two perpetual annuities, the pres- 
ent value of the one which begins immediately, interest 
being four per cent, is $2500, and that of the one which is 
deferred ten years is ^^, or $1689. Their difference is 
$2500 -$1689 or 811. Now such a difference as this, i.e. 
the difference between any particular sum (as $2500) and 



210 NATURE OF CAPITAL AND INCOME [Chap. XIII 

its discounted value for any time, is called the total discount 
on that sum. We may, therefore, express our result by 
saying that the present value of a terminable annuity is the 
total discount on a perpetual annuity of the same annual 
amount beginning when the terminable one ends.^ 

If the terminable annuity is itself deferred, its present 
value is the discounted value of its value reckoned at 
inception. 

§6 

Terminable annuities are sometimes employed by insur- 
ance companies and governments, but are otherwise com- 
paratively rare as specific forms of property rights. Ap- 
proximate cases, however, of such income exist in the case 
of many, if not most, durable articles of wealth. Thus, a 
machine yields a series of services of fairly uniform value for 
a fairly fixed term of years, and the same may be true of a 
house or other building, a ship, the rolling stock and other 
equipment of a railroad, etc. Such terminable income is 
also exemplified in many kinds of land, in the case of mines 
and quarries, peat beds and other tracts whose yield brings 
exhaustion. The state of Nevada presents an example of 
a large area of land which once yielded large incomes, but 
to-day is quite or nearly unproductive. It is evident, 
however, that in all these cases risk is an important factor 
in determining capital-value. This factor is for the present 
excluded from consideration. 

As the date for the termination of the annuity approaches, 
the total discount diminishes; hence, the capital- value of 
the terminable annuity diminishes. The decrease of capi- 
tal-value is what is sometimes known as ''wear and tear"; 
namely, the depreciation of an article due to the fact that the 
services left for it to render gradually diminish. The ap- 
proaching cessation of services may or may not be due to 
physical wear, so that the expression "wear and tear" is a 

^ For a mathematical presentation of this proposition, see Appen- 
dix to Chap. XIII, §§ 6, 7. 



Sec. 6] VALUE OF CAPITAL 211 

misnomer. We can imagine an article which suffers no 
material change, and of which the services will nevertheless 
last only a limited period. On the Atlantic coast the fish- 
ermen sometimes construct temporary platforms which 
are pretty sure to disappear in the September gales. It 
is evident that the value of such a property will decrease 
rapidly as the end of the fishing season approaches, without 
this decrease being due in the least to any physical deteriora- 
tion. The ''World's Fair" buildings at St. Louis depre- 
ciated, during the brief period of the fair, from $15,000,000, 
which was first paid for their construction, to $386,000, for 
which they were sold after they had served the purpose for 
which they were built. In like manner, a small wooden 
bridge, which is to be supplanted by a larger and better 
structure near by, will decrease in value rapidly as the time 
approaches for the other structure to divert its traffic, 
without any corresponding physical deterioration. Exam- 
ples are common enough of productive instruments losing 
their value, because of its being known that better devices 
are soon to displace them. ''Wear and tear," therefore, is 
a phrase which we must use only in a metaphorical sense. 
Even when the wear and tear take place because of physi- 
cal deterioration, this deterioration acts upon the value only 
in so far as it decreases or terminates the flow of income, 
and not because of a physical change in the capital which 
bears this income.^ The value of the capital depends ex- 
clusively on the income from it, and not directly upon its 
physical condition. 



Having considered the case of a terminable annuity, we 
turn to the case of a bond, which entitles the holder 
not only to a terminable annuity, but also to a single de- 
ferred sum called the " principal." Thus, a so-called " five 

* Cf. Bohm-Bawerk, Positive Theory of Capital, English translation, 
1891, p. 347. 



212 NATURE OF CAPITAL AND INCOME [Chap. XIII 

per cent, ten-year, $100 bond" means the right to receive 
an annuity of $5 a year for ten years, and, in addition, 
^100 at the end of the ten years. 

If the rate of interest is five per cent, and one buys a bond 
which entitles him to an annual income of $5 a year for ten 
years and $100 returnable at the end of this period, it is 
evident that the purchase price of the bond must be $100. 
In this case the $5 of annual income is the interest on the 
purchase price, and the sum of $100 which is to be received 
at maturity is equal to the originally invested capital or 
"principal." For these reasons such a bond is called a five 
per cent bond, the annual installments of income are called 
" interest," and the final payment of $100 is called "prin- 
cipal." 

But more often than not the bond is not sold at par ; con- 
sequently all of the three terms just mentioned are mis- 
nomers. If the bond is sold above par the rate of interest 
is not five per cent, but less than five per cent, so that it is 
only nominally a "five per cent bond"; the $5 annually 
received is only nominally "interest"; and the $100 re- 
turnable at the end is only nominally "principal." 

In order to obtain the capital-value of a so-called five 
per cent bond when the market rate of interest is four per 
cent {i.e. when the bond is sold on a four per cent basis), 
we need simply to add together the present values (reckoned 
at four per cent) of the ten payments of $5 and of the final 
payment of $100. We may consider these items as consist- 
ing of (1) a ten-year annuity of $5 a year, and (2) a sum of 
$100 deferred ten years. Both of these we can easily find 
from the explanations already given. 

It has been explained^ that the present value of a ten- 
year annuity is the "total discount" on the capitalized 
value of a corresponding perpetual annuity beginning when 
the terminable annuity ceases. Now a perpetual annuity 
of $5 is worth, if interest is four per cent, ;^, or $125.^ 

1 See § 5, supra. ^ See § 3, supra. 



Sec. 7] VALUE OF CAPITAL 213 

A perpetual annuity beginning in ten years will thus be 
worth $125 — in ten years. To-day, therefore, it is worth, 
by discounting at four per cent, (^^> or $84.45. The 
"total discount" is, therefore, $125 less $84.45, or $40.55. 
We need to add to this the other element in the bond, 
namely, the present value of the so-called "principal" of 
$100 due in ten years. Discounted at four per cent, this 
is worth (1^10, or $67.56. Combining our two figures we 
Lave, for the value of the bond, $40.55 + $67.56, or $108.11. 
We find, therefore, that a so-called five per cent bond 



yields the investor four per cent if it is bought at $108^^0. 
In like manner it could be shown that it will yield him six 
per cent, if bought at $92.50.^ 

In general a bond sells at par when the annual income, 
or nominal "interest," is equal to the true interest on the 
principal ; it sells above par if the annual income (nominal 
interest) is greater than the interest on the principal ; and 
below par if it is less. 

In a similar way we may calculate the value of a bond in 
cases where the installments of income, or nominal interest, 
are semi-annual and the rate of interest is reckoned semi- 
annually, and in the case of more frequent intervals, as well 
as in the limiting case of continuous payment.^ 

Elaborate tables have been constructed, called "bond 
value books," calculated on the foregoing principles, which 
are used by brokers for showing the value of bonds under 
different circumstances. The tables are usually employed, 
however, for the converse problem, to find the rate of in- 
terest "realized" when a bond is bought at a given price. 
The following is an abridgment of these tables, for (so- 
called) three per cent, four per cent, and five per cent bonds. 
The prices of the bonds in all cases are the prices taken 

^ For a mathematical statement, see Appendix to Chap. XIII, 
§ 8; for an alternative method of calculating the value of a bond 
and one which gives the "premium" separately, see Appendix to 
<:hap. XIII, § 9. 

^ For mathematical statement, see Appendix to Chap. XIII, § 10. 



214 



NATURE OF CAPITAL AND INCOME [Chap. XIII 



Rates of Interest 

(reckoned semi-annually) realized on a bond (with semi-annual cou- 
pons) known as a 

" Three per cent bond" 









Years to Maturit\ 








Price 




















1 


a 


3 


5 


10 


30 


30 


50 


120 












1.8 


2.1 


2.3 


110 










1.9 


2.4 


2.5 


2.6 


105 






1.3 


2.0 


2.4 


2.7 


2.8 


2.8 


103 




1.5 


2.0 


2.4 


2.7 


2.8 


2.9 


2.9 


102 




2.0 


2.3 


2.6 


2.8 


2.9 


2.9 


2.9 


101 


2.0 


2.5 


2.7 


2.8 


2.9 


2.9 


2.9 


3.0 


100 


3.0 


3.0 


3.0 


3.0 


3.0 


3.0 


3.0 


3.0 


99 


4.0 


3.5 


3.4 


3.2 


3.1 


3.1 


3.1 


3.0 


98 


5.1 


4.1 


3.7 


3.4 


3.2 


3.1 


3.1 


3.1 


97 


6.1 


4.6 


4.1 


3.7 


3.4 


3.2 


3.2 


3.1 


95 


8.3 


5.7 


4.8 


4.1 


3.6 


3.3 


3.3 


3.2 


90 




8.6 


6.7 


5.3 


4.2 


3.7 


3.6 


3.4 


80 








7.9 


5.7 


4.5 


4.2 


3.9 


70 










7.3 


5.5 


4.9 


4.5 



Ditto for a "Four per cent bond" 



Price 


Years to Mjvtority 


1 


3 


3 


5 


10 


30 


30 


60 


130 












2.2 


2.6 


2.9 


120 








1 


1.8 


2.7 


3.0 


3.2 


110 








1.9 


2.8 


3.3 


3.5 


3.6 


105 




1.5 


2.3 


2.9 


3.4 


3.7 


3.7 


3.8 


103 




2.5 


3.0 


3.3 


3.6 


3.8 


3.8 


3.9 


102 


2.0 


3.0 


3.3 


3.6 


3.8 


3.9 


3.9 


3.9 


101 


3.0 


3.5 


3.6 


3.8 


3.9 


3.9 


3.9 


4.0 


100 


4.0 


4.0 


4.0 


4.0 


4.0 


4.0 


4.0 


4.0 


99 


5.0 


4.5 


4.4 


4.2 


4.1 


4.1 


4.1 


4.1 


98 


6.1 


5.1 


4.7 


4.5 


4.3 


4.2 


4.1 


4.1 


97 


7.2 


5.6 


5.1 


4.7 


4.4 


4.2 


4.2 


4.1 


95 


9.4 


6.7 


5.8 


5.2 


4.6 


4.4 


4.3 


4.2 


90 




9.6 


7.8 


6.4 


5.3 


4.8 


4.6 


4.5 


80 








9.1 


6.8 


5.7 


5.6 


5.1 



Sec. 7] 



VALUE OF CAPITAL 



215 



Rates of Interest 

(reckoned semi-annually) realized on a bond (with semi-annual cou- 
pons) known as a 

" Five per cent bond " 









Yl 


Aiis TO Maturity 








Pkice 


















1 


3 


3 


5 


lO 


20 


30 


50 


140 












2.5 


3.0 


3.4 


130 




■ 






1.7 


3.0 


3.4 


3.7 


120 










2.7 


3.6 


3.9 


4.1 


110 






1.6 


2.8 


3.8 


4.3 


4.4 


4.5 


105 




2.4 


3.2 


3.9 


4.4 


4.6 


4.7 


4.7 


103 


2.0 


3.4 


3.9 


4.3 


4.6 


4.8 


4.8 


4.8 


102 


3.0 


4.0 


4.3 


4.6 


4.8 


4.8 


4.9 


4.9 


101 


4.0 


4.5 


4.6 


4.8 


4.9 


4.9 


4.9 


5.0 


100 


5.0 


5.0 


5.0 


5.0 


5.0 


5.0 


5.0 


5.0 


99 


6.1 


5.5 


5.4 


5.2 


5.1 


5.1 


5.1 


5.1 


98 


7.1 


6.1 


5.7 


5.5 


5.3 


5.2 


5.1 


5.1 


97 


8.2 


6.6 


6.1 


5.7 


5.4 


5.2 


5.2 


5.2 


95 




7.7 


6.9 


6.2 


5.7 


5.4 


5.3 


5.3 


90 






8.9 


7.4 


6.4 


5.9 


5.7 


5.6 


80 










7.9 


6.9 


6.5 


6.3 



immediately after an installment of income. They are 
what business men call "ex-interest" prices, i.e. are devoid 
of accrued interest. To use the tables when we have given 
the price at any time between two installments of income, 
it is necessary first to "strip" this price of the interest 
accrued since the last installment of income. 

It may be asked. Where is the line of demarcation be- 
tween what are nominally "principal" and "interest"? 
The answer is : None at all of any logical importance. 
In our calculations all the items receivable from the bond, 
including the principal when paid, have been treated on 
the same basis. They are, with respect to the bond, its 
true "income." The so-called "principal" is usually re- 
garded as a repayment of the original investment. Ap- 
proximately, the original investment and final "principal" 
are equal. But whether equal or not they are distinct. 



216 NATURE OF CAPITAL AND INCOME [Chap. XIII 

The original investment is the discounted value of expected 
receipts; the final "returned" principal is simply one (the 
largest one) of those receipts. The only difference between 
this large receipt and the other smaller ones is that, usually, 
it is employed differently when received. It is usually 
reinvested in other long-time securities, whereas the smaller 
items of income, the so-called "interest," are spent for arti- 
cles of shorter duration, and, thereby, soon converted 
into true "final income." The "principal" and "interest," 
therefore, while both are income with reference to the bond 
considered by itself, are apt to lead to different results when 
followed into the final transformations of purchase and 
sale, by the debit and credit cancellations previously ex- 
pounded. If we suppose a five per cent bond to be always 
sold on a five per cent basis, and the principal to be always 
reinvested in the same kind of security, it is evident, in 
relation to the whole series of operations, including the rein- 
vestment, that the principal, though income, is immediately 
canceled by reinvestment as outgo. In other words, 
whenever it appears as income from one bond, it 
immediately disappears again as outgo for another; con- 
sequently the owner is virtually in possession of a per- 
petual annuity of $5 a year. It is with a view to such an 
operation that the final payment of $100 on a bond is in- 
stinctively regarded on a different footing from the other 
payments called "interest." It is called "principal" on 
the theory that it is to be reinvested in order to continue 
the annuity of $5. It thus in theory represents capital, 
whereas the other payments represent only income. But 
we see now that both are income received from the bond 
as a source of income, although either may, by reinvestment, 
be put into capital. That one of them is usually put back 
into capital and the other not, is a matter of subsequent 
history and does not affect the immediate study of the 
bond itself. 

Even when the "principal" received at the maturity of 



Sec. 8] VALUE OF CAPITAL 217 

the bond is reinvested, it may be that it is not equal to 
the original investment, nor, therefore, to the capital-value 
of the bond at any time before maturity. This equality 
would hold true only in case the bond is always kept at 
par. When it is worth more or less than par the capital- 
value is more or less than the "principal," and for this 
reason, if for no other, the capital-value should not be 
confounded with the " principal." 

In order to determine whether or not a nominally five 
per cent bond really yields five per cent, we must refer to 
the price at which it sells, and while there is no neces- 
sity to abandon the terminology by which ''principal" 
and "interest" are used with reference to bonds, these 
terms are undoubtedly misnomers and their existence is 
responsible for considerable confusion. For instance, 
insurance companies have recently been offering their 
policy holders an option between the receipt at the death 
of the insured of a definite insurance of $1300, or of a 
"five per cent gold bond" for $1000. The gold bond has 
seemed, to many policy holders, a tempting form of invest- 
ment because of the " high rate of interest," — five per cent ; 
but it is evident that such a bond, considered as the equiva- 
lent of $1300 in cash, is on a lower basis than five per cent. 



Hitherto we have considered only four special cases of 
capitalizing income, viz. (1) the capital-value of a single 
income item ; (2) the capital- value of a perpetual annuity ; 
(3) the capital- value of an annuity terminable in a definite 
number of years ; and (4) the capital- value of a bond. But 
it is clear that the items of income from any property may 
occur in many other forms, may last for any length of time, 
and may be distributed through this time in any manner 
whatever. Let us, therefore, consider the general case in 
which any random series of income items, AB, A'B' , A"B" , 
A'"B''' , are received^ as shown in Figure 4. The capital- 



218 



NATUKE OF CAPITAL AND INCOME [Chap. XIII 



value of this series at the point of time is found by 
adding together the present value of the separate items. 
The best way to exhibit this is to begin at the last income 
payment, A"'B"'. Just after this last installment, of 
course, the property is valueless ; that is, its capital-value is 
zero. Just tefore this installment the capital- value is equal 
to the installment itself, and is represented by A"'B"' . At 

D 




Fig. 4. 

^ny time in the interval between this installment of income 
and the next preceding installment, the value will evidently 
be found by following the discount curve B"'C" , C" being 
vertically over A" . The height A"C" is, therefore, the 
capital-value of the property just after the payment A"B" . 
Its capital-value just before this payment is found by adding 
the vertical line C"D", equal to the installment of income 
A"B". From D" in turn we proceed backward along the 
discount curve D"C' to C, at which point A'C represents the 
capital- value of the property just after the installment A'B\ 
To this is added, if we pass back an instant, an amount 
CD' equal to the installment A'B'. The result is A'!/, 
the capital-value just before said installment. From D', in 



Sec. 8] 



VALUE OF CAPITAL 



219 



turn, the capital-value descends along the discount curve 
to C, where CD, equal to AB, is added, and from D we 
proceed finally by discount curve to P, vertically over 0. 
OP is, therefore, the capital-value of the property at the 
" present " instant, and its value at any succeeding in- 
stant is shown by following the course of the broken line 
PDCD'C'D"C"B"'A'"} This curve must descend to zero 



B' 



B 
Fig. 5. 

finally, when the income is exhausted, and it usually 
shows a tendency to decrease before this last payment 
is reached. 

If, in a series of income items, a negative one occurs, it is 
only necessary to reverse the capital curve, as shown in 
Figure 5, where the first installment, AB, is outgo instead 
of income. The curve PB" evidently represents the be- 
havior of capital- value, rising suddenly as the outgo AB 
is passed and falling when the income A'B' is received, 
and so on to the end. 

We may, if we choose, trace the history of the value of a 
security from the time immediately before its purchase, and 
consider the purchase price itself as an outgo. If this price 



^ For the mathematical formula for the capital-value of any series 
of income installments, see Appendix to Chap. XIII, § 11. 



220 



NATURE OF CAPITAL AND INCOME [Chap. XIII 



is exactly equal to the discounted value of the succeeding 
income, it is evident that the value immediately before its 
purchase must be exactly zero. Thus in Figure 6 let OM 
be the purchase price, and equal to OA, which is the capital- 
value immediately after purchase. The capital-value 
immediately before purchase is, therefore, zero, and the 
entire capital curve is the line OABCDEFH, which starts 




Fig. 6. 

at zero and ends at zero, but is above the zero line at all 
intermediate intervals. This represents the normal his- 
tory of any capital instrument if bought at a " fair 
price." 

If the flow of income is continuous, we may obtain the 
capital-value approximately by dividing the continuous 



Sec. 9] VALUE OF CAPITAL 221 

income stream into arbitrary installment sand discounting 
each installment separately/ 

The value of the income stream has heretofore been 
always reckoned in advance of its occurrence; that is, we 
have discounted income to obtain present value. We may, 
however, consider an income as paid for at the close of 
the period, in which case we have to deal with its "accu- 
mulated" value or its "amount." ^ 

§9 

Thus far we have considered the possibility of but one 
income stream from any given capital wealth. But it often 
happens that, with one capital instrument, there is a choice 
between various income streams. Land may be used for 
grazing, agriculture, building, or recreation purposes. 
Tools may be employed in a variety of ways, and the same 
is true of innumerable articles of wealth, particularly when 
taken in combination. What determines the choice of the 
series of uses to which any given instrument may be put ? 
Evidently that series of uses or income stream will be se- 
lected which yields the maximum present value. Thus, 
if land used for grazing purposes will yield a net service of 
$1000 a year forever, and interest is taken at four per cent, 
its value for grazing purposes is evidently $25,000. If, 
in like manner, the capital-value for some other use, say for 
growing wheat, is $20,000, it is clear that the land will be 
employed for grazing rather than for growing wheat. 

Sometimes the two series of uses to which land or other 
wealth may be put differ, not only in their amount, but in 
their time of beginning or ending. In a city, for instance, 
land may be used either for present dwelling or for future 
business-purposes, and it often becomes a question which 
use is the more valuable. In case the city is growing 

* For a fuller statement, see Appendix to Chap. XIII, § 12. 
^ For discussion, and for formulae for the capital-value of any in- 
come, discontinuous or continuous, see Appendix to Chap. XIII, § 13, 



222 NATURE OF CAPITAL AND INCOME [Chap. XIII 

rapidly, it may happen that in certain quarters, although 
the present use for dwelling purposes is more important, in 
a few years the locality will cease to be a residence quarter 
and the land will be needed for business purposes. In such 
cases, it may ''pay" to keep the land out of present use en- 
tirely and reserve it until the city has grown so as to make 
it profitable to erect a business block. If the land were now 
encumbered with a dwelling, either the possibility of its 
subsequent use for business purposes would be cut off, 
or the profit from its conversion to those purposes would be 
impaired by the prior destruction and waste of the dwelling. 
Under such circumstances it would usually happen that 
speculators would buy up and hold the land. The manner 
in which the gain presents itself to them is simply as a pro- 
spective rise in value from the growth of the city; they 
therefore buy the land to sell it later at a higher price. 
Such a speculator is commonly regarded as keeping land 
"out of use." He is, however, only deferring the use, and, 
if he has foresight, is no more to be condemned than the 
wise speculator on the wheat exchange, whose work, as is 
well known, operates to conserve the supply of wheat. The 
speculator thus tends to bring about the best utihzation of 
the land in the sense that, out of several alternative income 
streams which the land might be made to yield, that one is 
selected which possesses for him the maximum present 
value. In general it is probable that the best uses of the land 
for the public also are found in this way. The latter con- 
clusion does not, however, absolutely follow from the former, 
since the " best " uses are not necessarily those which 
have the greatest market value; but those who would 
prevent all land speculation will at least need to adduce 
other arguments than that speculation "keeps land out of 
use," before they have- proven their case; for wise land 
speculation means simply the discriminating choice, out of a 
number of uses, of that use or series of uses which affords 
to-day the greatest present value. 



Sec. 10] VALUE OF CAPITAL 223 

It should be observed that if the rate of interest is raised, 
the relative advantages of the two uses in the example 
given might be quite different. In this case it might pay 
to put up the dwelling rather than wait for the business 
block ; for the holder of the land, as he expresses it, could 
not afford to "lose his interest" when it is at so high a rate. 

§10 

Thus far we have considered the capital-value only of 
individual articles of wealth. The same reasoning applies 
to a group of articles of wealth. An important case is 
that of a merchant's stock. In this case we may prefer 
to capitalize the stock as a whole rather than to take 
the sum of the capitalizations of its separate elements. 
The net income from the stock is found by subtracting 
from the gross income all the outgo, including, besides 
the cost of replenishing the stock, the other costs of the 
business, — clerk hire, rent, and even an allowance for the 
work of the merchant himself, unless he is a mere "silent 
partner." If the net income is supposed to remain constant 
forever, the capital value of the stock will, of course, be 
found by dividing the net income by the rate of interest. 
In this case the rate of interest must be taken for the proper 
installment interval. If the goods are supposed to be con- 
tinuously bought and sold, the rate to be employed is the 
"rate of interest per annum reckoned continuously." ^ 

§11 

We conclude, therefore, that the value of any capital- 
good, either of wealth or of property-rights, assuming that 
all future income is foreknown, is the discounted value of 
that income, and consequently that, as time goes on, the 
value of that capital will oscillate, rising gradually during 
intervals between installments along a "discount curve," 

^ For a mathematical statement in this connection, see Appendix 
to Chap. XIII, § 14. 



224 NATURE OF CAPITAL AND INCOME [Chap. XIII 

as the future income approaches, and falling suddenly as the 
installments are successively passed by and acting in a 
contrary manner before and after an outgo. This os- 
cillation of capital-value ends finally at zero, when the 
life or service of the article or group is ended. It also often 
begins at zero, when the instrument or group is one that is 
newly acquired or produced. These changes constitute, 
as it were, a sort of life history of capital- value. ^ 

It may seem to some readers that there is an exception 
to the rule that the value of capital is the discounted 
value of its expected income, in the case where the 
income which might be received from the capital is in- 
definitely postponed. This is the case in which the "prin- 
cipal" accumulates at compound interest so that no " in- 
terest" is withdrawn. If a person has a deposit of $1000 
in a savings bank and leaves it there to accumulate at 4 
per cent until it amounts to double that sum, which will 
happen in about eighteen years, the $1000 does not appear 
to him to be the discounted value of any income. If he 
thinks of it as the discounted value of anything at all, it 
will be of the $2000 of capital which he expects to own at 
the end of eighteen years. It is perfectly true that the 
capital-value of $1000 is the discounted value of the future 
capital-value of $2000; but the latter capital-value is 
itself the discounted value either of some subsequent 
income, or, in turn, of a capital still further deferred, and 
so on indefinitely. Actual income is hoped for some- 
time, even if it be not for a million years. The present 
$1000 is the discounted value of that ultimate income, how- 
ever far distant. A perpetual accumulation is, humanly 
speaking, out of the question. But if such perpetual 
accumulation be regarded for the moment as possible, it 
may still be interpreted as a perpetual postponement of 
possible income; so that even in this case the $1000 may 

^ For mention of the case where the rate of interest changes and its 
changes are foreknown, see Appendix to Chap. XIII, § 15. 



Sec. 11] VALUE OF CAPITAL 225 

still be regarded as the discounted value of an income 
which is indefinitely postponed, but indefinitely great. Of 
course, such a limiting case is of purely theoretical interest. 
The prodigious sums which result from the reckoning of 
compound interest always surprise those who have never 
made such computations. One dollar put at compound 
interest at 4 per cent would amount, in one century, to 
$50, in a second century to $2500, in a third century 
to $125,000, in a fourth century to $6,500,000, in a 
fifth century to $325,000,000, and in a sixth century to 
$16,000,000,000. Beyond this the figures are ahnost 
unthinkable in magnitude.^ 

Yet we have few instances in which any one has endeav- 
ored to set aside even one dollar for the benefit of posterity 
six centuries removed ! There is too much reluctance to 
build for the remote future, even though the attainable 
results are enormous. Benjamin Franklin, at his death 
in 1790, left £1000 to the town of Boston and the same sum 
to Philadelphia, with the proviso that it should accumulate 
for a hundred years, at the end of which time he calculated 
that at 5 per cent it would amount to £131,000. In the 
case of the Boston gift, it actually amounted, at the end 
of the century, to $400,000, and has since accimiulated to 
about $600,000. The sum received by the city of Phila- 
delphia has not increased nearly as fast. 

Another interesting case of accumulation is that of the 
Lowell Institute in Boston, which was founded by a bequest 
of $200,000 in 1838, with the condition that 10 per cent of 
the income from it should be reinvested and added to the 
principal. The peculiarity of this provision is that it 
applies in perpetuity. There is, therefore, theoretically no 
limit to the future accumulation thus made possible. 
The fund, after sixty-seven years, amounts already to 
$1,100,000. 

It must be remembered however that practically even a 

* For a geometrical representation, see Appendix to Chap. XIII, § 16. 
Q 



226 NATURE OF CAPITAL AND INCOME [Chai-. XIII 

small sum, such as $1000, if allowed to accumulate, let us 
say, at 4 per cent for 1000 years, could never actually 
attain the theoretical magnitude. This is evident from 
the fact that the theoretical sum would then amount to 
over $100,000,000,000,000,000, which is so far in excess of 
the total value of capital on this planet, as to be out of 
the range of possibility. The reason the sum would fail 
to accumulate as fast as theoretically required, aside from 
fortuitous losses, lies in the reduction of the rate of in- 
terest which the very accumulation would bring about. 
The administrators of such a fund, as the centuries passed 
by, would jfind it increasingly difficult to obtain fields in 
which to invest it, and their effort so to invest would have 
the same effect in reducing the rate of interest realized on 
the investments as is now felt by the national banks in 
their pressure to buy government bonds. 



CHAPTER XIV 



EAENINGS AND INCOME 



§1 

In the last chapter it was shown that, perfect foresight 
being assumed, the value of any capital good is derived from 
its future income by discounting the value of that income. 
It now remains to compare the capital-value thus derived 
with the expected income- value on which it depends. 

It is evident at the outset that the capital-value is less 
than the total expected income; for the discounted value 
of any future sum is necessarily less than that simi itself. 
This fact is illustrated in the third and fourth columns of 
the following table of capital and income in the cases of 
five typical articles : — 









Capital- 


Capital- 


Capital 


Net Income per Year 


Income 


TALUE (Int. 

AT 5%) 


value (Int. 

AT 11%) 


Land 


$1000 per year for- 










ever 


Infinite 


$20,000.00 


$40,000.00 


House 


$1000 per year for 










50 years .... 


$50,000.00 


18,300.00 


28,400.00 


Horse 


$100 per year for 










6 years .... 


600.00 


508.00 


551.00 


Suit of 


$20 1st year; $10 








clothes 


2d year .... 


30.00 


28.00 


29.00 


Loaf of 


$36.50 per year, for 








bread 


1 day .... 


.10 


.10 


.10 



In this table we observe that the value of the land, when 
interest is at 5 per cent, is $20,000, whereas the total in- 
come to be expected from it is infinitely greater; that the 

227 



228 NATURE OF CAPITAL AND INCOME [Chap. XIV 

value of the house when interest is at the same rate is 
$18,300, whereas the total income to be expected from it is 
about three times as much, or $50,000 ; that the value of 
the horse is a little over $500, whereas the total expected 
income is about $100 more, or $600; that the value of the 
suit of clothes is $28, whereas its total income is $30, of 
which $20 accrues the first year and $10, the second; and, 
finally, that the capital-value of the loaf of bread is 10 
cents and the income expected from it is also 10 cents. 
In this limiting case there is practically no diminution on 
account of the interval of time to elapse between the time 
of valuing the instrument and the time of receiving its 
services, for the reason that this time is too brief. 

From the table we see clearly one reason that certain 
articles have been identified with income and others 
not. Bread has practically the same capital- value as 
income- value, so that, if a person were not accustomed to 
fine distinctions, he might think it unnecessary to discrimi- 
nate between the 10 cents which is the value of the use of 
the bread, and which is, therefore, income^ and the 10 cents 
which is the value of the bread itself, and which is, therefore, 
capital. There is almost as much danger of such confusion 
in the case of clothing ; for there is only a slight difference 
between the $30 which is the value of the use of the suit, 
and is therefore income, and the $28 which is the value of 
the suit, and is therefore capital. But as we pass to the 
more enduring articles, there emerges so wide a difference 
between the value of the use of an instrument and the value 
of the instrument itself, that there is no difficulty in dis- 
tinguishing between them. Accordingly we usually find in 
treatises on economics some distinction between the value 
of the use of a house ($50,000 in the foregoing table) and 
the value of the house itself ($18,300 in the table). But if 
the distinction is valid in one case it is valid in the others. 
The consequence of disregarding it we have already seen 
in Chapter VII. 



Sec. 2] EARNINGS AND INCOME 229 



If the rate of interest is not 5 per cent, but 2^ per cent, 
there will result great differences in the capital- values. 
The consequences are seen in the last column of the 
table. But the effect on capital-values wrought by thus 
-cutting the rate of interest in two will be different for each 
of the five different articles. The more enduring ones will 
be affected the most. When the rate of interest is halved 
the value of the land will be doubled, rising from $20,000 to 
$40,000, but the value of the house will rise by only about 
60 per cent, i.e. from $18,300 to $28,400 ; the value of the 
horse will rise only 10 per cent, i.e. from $508 to $551 ; the 
value of the suit will rise only from $28 to $29 ; and, finally, 
the value of the loaf of bread will not rise at all, but wiU 
remain at 10 cents. We see in these five types of articles 
that the sensitiveness of capital-value to a change in the 
rate of interest is the greater the more enduring the income. 

In general, also, this sensitiveness is the greater the more 
remote the periods of time at which the income is concen- 
trated. For instance, if the total income is $100, and is 
all concentrated at a point of time fifty years distant, its 
capital-value, when the rate of interest is 5 per cent, is $8.72, 
but it becomes $29.09 when the rate of interest is reduced to 
2^ per cent. That is, the rate of interest being halved, the 
capital-value is more than trebled. If the same income of 
$100 were to be due only one year from date, the change 
from 5 per cent to 2^ per cent in the rate of interest would 
elevate the capital- value only from $95 to $97.50. 

§3 

Thus far we have been concerned only with total income, 
in relation to capital- value ; we now consider the rate of 
income per year in relation to capital-value. This ratio 
lias already been called the rate of "value-return." 

In accordance with previous explanations the sequence 



230 NATURE OF CAPITAL AND INCOME [Chap. XIV 

of calculating the rate of value-return is as follows: 
A specified property entitles the owner to a future series of 
income items which is assumed to be definitely foreknown. 
These items are all discounted by means of a specified rate 
of interest. The sum of the discounted values constitutes 
the capital- value of the property. This capital- value, at 
any time, taken as divisor and the income per year taken as 
a dividend gives the rate of value-return as quotient. 

It must be steadily borne in mind that the value of the 
capital which forms the divisor is not a fictitious book 
value, nor the value as indicated by the sum of money 
originally invested, but is simply the discounted value, at 
the specified time, of the expected income subsequent to 
that time. We should at the outset rid our minds of 
the bogey of an unvarying "principal" perpetually existing 
somewhere in a debt or other property. The only value 
entity we have to deal with is the value of the property 
considered, which is the discounted value of the expected 
income, and which therefore is continually changing. 
When capital is for the present yielding no income, as, 
for instance, vacant land, it nevertheless is expected some- 
time to yield income, and it is the discounted value of this 
remote income which alone constitutes the present value 
of the land. It is true that a speculator may prize the 
land simply because he thinks he can sell it later to some 
one else, and to him it may seem that its value is inde- 
pendent of any future income, and depends only on the 
future capital- value at which he expects to sell. But it is 
clear that this futuref' capital- value is itself the discounted 
value of the income which the then purchaser will expect. 
Or, if he too be a speculator, and his valuation, hke his 
predecessor's, depends on a resale, the dependence on 
future income is merely again postponed to the time when 
some purchaser shall buy the land for the income it will 
yield. This ultimate expected uicome gives the basis for 
all prior capital valuations. Were there no expectation 



Sec. 4] EARNINGS AND INCOME 231 

of any future income — or, at least, the expectation that 
there would be an expectation of it — there could be no 
capital-value. Capital-value, independent of expected in- 
come, is impossible. 

§4 

MJThe first proposition to be emphasized as to the rate of 
value-return is that it is not necessarily equal to the rate of 
interest, but may be either greater or less than that rate, and 
to any degree. 

Let us take, for example, the case of the house which we 
assumed would endure just fifty years, giving throughout 
that period a shelter-service worth, after actual expenses 
are deducted, $1000 annually. We saw that its value, 
computed by discounting this fifty-year annuity on a 5 per 
cent basis, is $18,300. It therefore yields the first year a 
rate of value-return on its capital-value of j|^, or 5.4 per 
cent. At the end of ten years its value, found by dis- 
counting the income still remaining, will be $17,200. It 
will therefore then be yielding a value-return of j^ per 
year, or 5.8 per cent. At the end of thirty years, in like 
manner, it will be worth $12,500 and yielding j^„, or 8 per 
cent. Again, the suit of clothes which will last two years, 
and gives services worth $20 the first year and $10 the 
second, has a value at the start of about $28, and at the end 
of the first year of about $9.50. The value-return the first 
year is therefore |, or 71.4 per cent, and the second year 
9^0, or over 100 per cent. The loaf of bread has a value 
of 10 cents. It yields 10 cents' worth of income in a day, 
which is at the rate of $36.50 per year ; consequently its 
value-return is ^, or a rate of 36,500 per cent per annum 
(interest reckoned daily or ''continuously"). 

In these examples the value-return exceeds the rate 
of interest. Reversely, it is possible for the value-return 
on capital to be less than the rate of interest. If, for in- 
stance, forest land with small trees is bought, it may be 



232 NATURE OF CAPITAL AND INCOME [Chap. XIV 

that no product can be obtained until the end of ten years.. 
We may suppose that then the yield is worth $1000 a year 
during the ensuing (second) decade, after which it will be 
worth $2000 a year forever. It may be shown that the 
present value of the forest, reckoned on a five per cent basis, 
is about $20,000. This would be the discounted value of an 
annuity of $1000 a year, whose commencement is deferred 
ten years from the date of investment, and which then 
runs ten years, plus the discounted value of a perpetual 
annuity of $2000 a year beginning twenty years in the 
future. On the five per cent basis, the forest will, 
in ten years from the present, be worth about $32,000 
(this being the discounted value of an immediate ten-year 
annuity of $1000 followed by a perpetuity of $2000).. 
Twenty years from the present, the forest will be worth 
$40,000 (this being the discounted value of $2000 a year 
forever). The forest land therefore rises gradually in value 
from $20,000 to $32,000 in the first decade, during which no 
income is realized, and continues to rise, though less rapidly, 
to $40,000 in the second decade, during which there is 
realized the comparatively small income of $1000 a year. 
The rate of return, therefore, at the beginning, being the quo- 
tient of the income realized divided by the capital, is jpoo, 
or zero. The rate of return evidently remains zero through- 
out the first decade. At the beginning of the second decade 
the rate is evidently ~^, or 3.1 per cent; at the beginning 
of the third decade it is ^, or 5 per cent. We see, 
therefore, that in this case the rate of value-return gradually 
rises from zero to a height equal to the rate of interest. 

There may even be a negative rate of return. A colt, for 
instance, may occasion more trouble than it is worth for the ^ 
first year, and produce a net expense or disservice of $20_J^ 
Thereafter it may render a net income of $10 during the 
second year, $20 during each year from the third to the 
tenth inclusive, and $10 a year the next five years, after 
which it dies. Supposing, as our preliminary hypothesis 



Sec. 4] 



EARNINGS AND INCOME 



233 



obliges us to do, that all these are definitely foreseen at the 
start, the colt would be worth the discounted value (at 5 
per cent) of all these, or about $135. It will therefore 
yield during the first year a return of ^, or — 15 per cent. 
The value-return for the second year, reckoned on its capital- 
value taken at the beginning of that year, is ^, or 6 per 
cent; on the third year ^, or 13 per cent, on the fifteenth 
year about jg, or 100 per cent. The entire series may be 
seen from the following table : — 



Income 
DTJKING Yeab 



Capital- 
value AT 
Beginning of 
Year 



Rate 
OF Retubn 



1st year 

2d year 

3d year 

4th year 

5th year 

6th year 

7th year 

8th year 

9th year 

10th year 

11th year 

12th year 

13th year 

14th year 

15th year 



;20 
10 
20 
20 
20 
20 
20 
20 
20 
20 
10 
10 
10 
10 
10 



$134 

161 

159 

146 

134 

121 

107 

92 

76 

60 

43 

35 

27 

19 

10 



-15% 
6 
13 
14 
15 
17 
19 
22 
26 
34 
23 
28 
37 
54 
100 + 



C^ From the foregoing examples it is evident that a prop- 
erty which yields 5 per cent to the investor may yield in 
individual years either more or less than 5 per cent. The 
dwelling house jdelded more than 5 per cent for 50 years, 
and then ceased to yield income. The forest yielded less 
than 5 per cent for 20 years, and thereafter yielded 5 per 
cent on its value at that time. The colt yielded rates ris- 



234 NATUKE OF CAPITAL AND INCOME [Chap. XIV 

ing from — 15 per cent in the first year to 100 per cent in 
the fifteenth year, and then zero forever after. 
n At this juncture, however, the business reader may feel 
disposed to object. He will point out that in our tables the 
house is represented as yielding 5.4 per cent the first year 
instead of 5 per cent, by neglecting depreciation, and 
that, contrariwise, the forest was represented as yielding in 
the eleventh year 3.1 per cent instead of 5 per cent, by 
neglecting appreciation. For it is true that the house, 
worth $18,300 at the beginning of the year, must, under the 
given conditions, depreciate $85 during the year; and the 
objector will maintain that this ought to be deducted from 
the $1000 received from the house, in order to obtain the 
true "net earnings." The deduction leaves $915, which is 
just 5 per cent on the capital of $18,300. According to this 
calculation, therefore, the house really returns, not 5.4 per 
cent, but only 5 per cent. And, applying the same line 
of reasoning to the case of the forest, the objector might 
insist that the forest increased in value just enough to 
make up the difference between the 3.1 per cent, which was 
given as the rate of value-return at the beginning of the 
second decade, and the 5 per cent to which it would seem 
to be entitled. 

These calculations are correct. But they do not mili- 
tate against the treatment of value-return which has been 
given. They merely bring into relief a distinction between 
income which is realized by the investor and income which 
is earned by the capital. Realized income is the value of 
the actual services secured from the capital; earned in- 
come is found by adding to realized income the increase 
of capital-value, or deducting from it the decrease. We 
may designate them briefly simply as income and earnings. 
To illustrate this distinction and to show its importance, 
let us consider a four per cent $1000 bond, the interest on 
which is payable annually. From what was shown in the 
previous chapter it is clear that (if the bond is valued on a 



JSec. 4] EARNINGS AND INCOME 235 

four per cent basis) the value of the bond will oscillate 
between $1000 and S1040, rising gradually from the former 
to the latter between interest payments and falling back 
suddenly as each payment is made. The income is simply 
the payment of $40 at the end of each year. Even our 
objector will not deny this. During the entire year up to 
the very end there is no income at all; yet the bond 
"earns" about $10 each quarter, in the form of an increase 
in the value of the bond. These earnings are simply equal 
to the interest on the capital. And so in general, when 
^e assume that income is definitely foreknown, earnings 
will equal the interest on the capital. It is, therefore, 
to earnings that accountants instinctively give their main 
attention. But they err grievously when they attempt to 
spirit away realized income and put earned income in its 
place. Realized income plays the more important role, for 
on it depend all the other elements, — capital- value, value- 
return, depreciation, and even earnings themselves. To 
take the case of the house, the first and primary fact is that 
it promises to yield $1000 a year for fifty years. This income 
series being given, it is possible to obtain its capital- value 
by the discounting process ; its value-return, by division of 
income by capital ; its depreciation, by comparing its capital 
values at successive dates; and its earnings, by deducting 
depreciation from realized income. Unless the realized 
income be given at the start, all these calculations are im- 
possible. Earnings could not serve as our starting point, 
for earnings cannot be calculated except by the aid of de- 
preciation, depreciation cannot be calculated except from 
capital- value, and capital- value cannot be calculated except 
from expected realized income. 

Moreover, the fundamental proposition of the last chap- 
ter, that capital-value is the discounted value of expected 
income, will cease to hold true, if by income we mean 
earniags. Thus, the house has a capital-value of $18,300, 
"Which is the discounted value of its realized income of 



236 NATURE OF CAPITAL AND INCOME [Chap. XIV 

$1000 a year for 20 years, discounted at 5 per cent. But 
it is not true that $18,300 is the discounted value of the 
earnings of the house, for the earnings are all less than 
$1000, beginning at $918 a year and dwindling each year 
until the fifty years have expired; and clearly the dis- 
comited value of fifty annual items each less than $1000 
must be less than the discounted value of fifty annual items 
of $1000 each. 

Since, then, earned income cannot be derived without 
assuming realized income, and since capital-value has been 
shown to be the present value of the latter, and not of the 
former, it is clear that realized income is the more fimda- 
mental concept of the two. y\y^ 

§5 

' But so persistent is the accountant's instinct to put aside 
realized income in favor of earnings that we need to point 
out in detail the confusions which arise, unless income and 
earnings are carefully distinguished. We first observe that, 
under the given conditions of foreknowledge, earnings and 
interest are equal. Now if interest is at 5 per cent, a capi- 
tal of $1000 invested in whatever form — land, houses, 
horses, securities, or anything else — though it is said to 
earn 5 per cent, does not necessarily receive an income each 
year of $50. The $1000 means the present value, dis- 
counted at 5 per cent, of some expected income stream; 
but that income stream may take any one of an indefmite 
number of forms; such, for instance, as a perpetual annu- 
ity of $50 a year, as in the case of land ; or a terminable 
annuity of $100 a year for 14 years ; or an income of $25 a 
year for 10 years followed by an income of $167.50 a year 
for 10 years. All of these are inter-equivalent, and when 
discounted at 5 per cent, each of them represents a capital 
of $1000. 

Of all these possible forms of income it is usual to take the 
perpetual annuity as the standard income (earnings) and to 



Sec. 5] EAKNINGS AND INCOME 237 

compare other incomes with iti Consider, for instance, the 
possessor of a property yielding $100 a year for 14 years. 
He will, if he discounts this income at 5 per cent, value that 
property at $1000. He thinks of himself as possessing 
$1000 ''invested in" that property. From it he gets the 
income of $l00 a year for 14 years. But he knows that he 
might sell this property for $1000 and reinvest in another 
property yielding the standard $50 a year forever. Con- 
trasting with the standard income of $50 a year forever 
which he might receive, the income of $100 a year for 14 
years which he does receive, we observe that at first his in- 
come is double the earned or standard income, being $100 
instead of $50. The excess of $50, however, is compen- 
sated for by a reduction of $50 in the capital-value of his 
property, for at the end of the first year the value of his 
property will be the discounted value of $100 a year for 
thirteen (instead of fourteen) years, which, if interest is 
still reckoned at 5 per cent, is $950. And so it is in general 
that the owner of $1000 invested at 5 per cent can obtain a 
higher income than the standard $50 only at the cost of 
trenching on capital to the extent of the excess. 

Suppose, on the contrary, that the $1000 is invested at 
5 per cent, but in such a form as to yield at first less than 
$50, e.g. in a form which yields the above-mentioned in- 
come of $25 a year for 10 years, followed by $167.50 a year 
for 10 years. In that case, during the first year the owner 
receives only $25 instead of $50, which is the earned or 
"standard" income. But the deficiency of $25 in his in- 
come is made up by an augmentation of his capital by that 
amount. 

The principle is perfectly general, and perhaps too 
familiar to require a rigorous demonstration, though there 
is no difficulty in framing on^^J We may therefore state : — 

(1) When a property yields a specified foreknown income, 
and is valued by discounting that income according to a 
specified rate of interest, if the income realized is equal to 



238 NATURE OF CAPITAL AND INCOME [Chap. XIV 

the income earned (and hence equal to the rate of interest), 
the value of the capital will remain at a uniform level. 

(2) If realized income exceeds earned income, the value 
of the capital will be decreased by the amount of the 
excess. 

(3) If realized income is less than earned income, the 
value of the capital will be increased by the deficiency.. 

These principles hold true whether the period for reckon- 
ing or compounding interest is a year, half year, quarter, or 
any other period, or shrinks to the vanishing point in the 
case of continuous interest. A slight modification or 
quahfication in the statement of these principles is, how- 
ever, necessary when, instead of there being a rate of in- 
terest which remains the same year after year, there is a 
succession of different rates.^ 
<^ Expressed in a single sentence, the general principle 
connecting realized and earned income is that they differ 
by the appreciation or depreciation of capital. It is thus 
possible to describe earned income as realized income less 
depreciation of capital, or else as realized income plus 
appreciation of capital. We may therefore state anew the 
fallacy of confusing realized income with earned income: 
the fallacy consists in reckoning depreciation of capital 
as a part of outgo, or appreciation of capital as a part of 
income. This usage is difficult to combat, for with many 
it has become habitual. To expose the fallacy completely 
will be our object during the remainder of this chapter. 

We may at the outset emphasize a fact already mentioned 
in Chapter VII ; namely, that this popular and erroneous 
usage is not consistently adhered to. A pension is an 
income the capital-value of which is continually diminish- 

^ The case is discussed in the Appendix to Chap. XIV, § 1. For 
practical purposes, however, this is a refinement into which we sel- 
dom need to enter. 



Sec. 6] EARNINGS AND INCOME 239 

ing. Yet even popular usage seldom or never deducts this 
depreciation from the pension to obtain the ''true" in- 
come; and the reason we instinctively include (as we 
ought) the whole of such a pension in income, is that 
the depreciation is not actually offset. In ordinary busi- 
ness, on the other hand, we are accustomed to deduct 
depreciation, because this is usually offset by actual pay- 
ments into a depreciation fund. Even in this case the 
depreciation is not itself an expense; but there is a con- 
comitant expense approximately equal to it, in the form of 
payments into the depreciation fund. It thus makes all 
the difference in the world whether the depreciation fund is 
actually maintained, or merely reckoned. If a deprecia- 
tion fund is actually maintained, the expense of maintain- 
ing it serves to reduce realized income so as to make it 
coincide with earned income. In such a case, therefore, the 
ideal earned income becomes realized in actual fact. 
C Assuming a fixed rate of interest, the depreciation fund 
may be defined as a fund formed by accumulating that 
part of income which must be turned back into capital in 
order to maintain the value of capital at a fixed level. A 
depreciation fund is thus made from annual contributions 
equal to the excess of realized income above earned in- 
come. If, instead of an excess, there is a deficiency, the 
contributions to the depreciation fund become negative, 
that is, instead of a certain quantity of income being con- 
verted into capital, a certain quantity of capital must be 
converted into income .^^^ 

Geometrically, a depreciation fund is very simply repre- 
sented. In Figure 7 let the income consist of the items 
a, a', a", a"', d'^, etc. The capitalized value of this in- 
come stream is AB. The interest on AB is represented by 
the height AC, so that the standard income would be 
represented by a series of annual hues of the height of the 
dotted line CD. The excess of the lines a, a' , a", etc., 
above the dotted line CD therefore represents the contri- 



240 



NATURE OF CAPITAL AND INCOME [Chap. XIV 



butions to the depreciation fund. Where there is a defi- 
ciency, as in the case of a'", the contribution to the 
depreciation fund is negative; that is, for that particular 
time, instead of some of the income being reinvested, some 
of the capital is used as income, to prevent income from 
falling below the uniform level prescribed for it. The same 



a' 



I a "I 



a'v 



av 



a VI 



I a VII 



Fig. 7. 



principles apply in case the income is a continuous flow, as 
shown in Figure 8. Here the earned income is represented 
by the elevation of the straight line CD, and the reahzed 
income by that of the curved hne EF ; the deprecia- 
tion fund is formed from the successive differences be- 
tween these elevations. Thus, if $1000 of capital is in- 
vested on a 4 per cent basis, but so that the returns are 
not $40, but $70 a year for twenty- two years, the annual 



Sec. 6] 



EAKNINGS AND INCOME 



241 



contribution to the depreciation fund is evidently 
For at the end of the first year, before the income is re- 
ceived, the capital-value will, under the supposed condi- 
tions, become not $1070, but only $1040. The first item 
of income, $70, is then received. This being deducted 
from $1040 leaves $970, which is $30 short of the original 




Fig. 8. 



capital-value. Consequently it is necessary to restore $30 
to the capital, in order to bring it up to the original level of 
$1000. 

It will evidently make no difference whether the income 
items are reinvested simply as additions to the original 
capital, or invested at the same rate of interest in some other 
form of capital. The owner of depreciating machinery may 



242 NATURE OF CAPITAL AND INCOME [Chap. XIV 

offset that depreciation by investing annually in a few 
new machines, or by annually buying investment securities. 
The latter type of investment is usually thought of when 
the phrase "depreciation fund" is used. If the owner 
of the machines follows this procedure, then instead of 
the original capital being maintained at a fixed level, it is 
continually decreasing, while the depreciation fund is con- 
tinually increasing in such a manner that the value of the 
two together — the machinery and the depreciation fund 
— remains constant. Consequently, at the end of the 
income term, when the value of the original capital, the 
machinery, is entirely exhausted, the value of the depre- 
ciation fund in securities will have exactly taken its place. 
This fact is sometimes employed in the definition of a 
depreciation fund. The fund is then described as formed 
of a succession of payments out of income, such that if 
each be accumulated at compound interest the total will 
equal the original capital at the end of the entire income 
term. 

The most common application of a depreciation fund is 
to a bond which does not sell at par. For instance, a. 
$100 five per cent bond, when interest is 4 per cent, will, if 
it has 20 years to run, sell at $115. The interest at 4 per 
cent on this capital is $4.60, which shows that the deprecia- 
tion fund, being the difference between the income and the 
interest, is $5 minus $4.60, or 40 cents. This item of 40 
cents should annually be saved out of the income and rein- 
vested at 4 per cent, in order that at the end there may 
still remain a capital of $115. If the last installment of 
income from the bond, $105, is treated as an income Hke 
the previous items, the depreciation fund is, in the last 
year, $105 minus 84.60, or $100.40 ; that is, besides the 40 
cents annually there should be reinvested, at the end of 
the term of the bond, the $100 of so-called "principal.'^ 
Thus we again reach the reason that the $100 of the last 
payment is regarded as "principal" or "capital" and not 



Sec. 7] EARNINGS AND INCOME 243 

"income." It is simply that this $100 is always supposed 
to enter into the depreciation fund, that is, to be rein- 
vested and not retained as income. In case the bond is 
sold at par {i.e. if it yields an income equal to the 
market rate of interest), there is no depreciation fund ex- 
cept the "principal" itself at the end, when the last item 
of realized income ($105) exceeds the earned income of 
$5 by $100. This excess, being reinvested at the same 
rate, 5 per cent, will secure the continuance of the same 
income. 

The operation of the depreciation fund presupposes that 
it is possible to invest the small differences each year in such 
a manner as to accumulate at compound interest at the 
rate which the original capital is earning. Such is not al- 
ways the case, especially with articles of wealth, like land, 
machinery, and so forth. In case two different rates of in- 
terest are involved, one for computing the capital-value of 
the given income, and another for compounding the annual 
savings put into the depreciation fund, the calculation of 
the depreciation fund will, of course, be more complex.^ 

§ 7 

In close relation to a depreciation fund is the "sinking 
fund" employed by governments as a means of meeting 
large obligations — in particular of meeting the "principal" 
of public debts. Needless obscurity has enveloped the 
"sinking fund," especially since the intricate but fallacious 
theories of Price and Pitt. 

The annual contribution to the depreciation fund was the 
difference between the income actually experienced and 
an ideal perpetual annuity of the same present value. 
A sinking fund, however, is formed from the difference 
between income (or more commonly outgo) actually expe- 

* The reader is referred to the Institute of Actuaries' Text-book, 
Part I, London (Layton), 1901, where this and other problems in an- 
nuities are fully dealt with. 



244 NATURE OF CAPITAL AND INCOME [Chap. XIV 

rienced and an ideal terminable annuity of the same present 
value. A government has to meet a series of expenses 
connected with its bonded debt. These expenses constitute, 
let us say, a stream of outgo lasting ten years, and consisting 
of nine equal payments — nominally "interest" — and one 
much larger payment, exceeding the others by the amount 
of the so-called "principal." The sinking fund is merely a 
device for equaUzing all ten payments. If the actual pay- 
ments are S5000 a year for nine years and $105,000 in the 
tenth year (as is the case of 10-year "five per cent" bonds), 
the ideal 10-year annuity equivalent to this series would, 
on a 4 per cent basis, be $13,329. The government, there- 
fore, if it would pay off its debt, or rather provide for it in 
ten equal installments, must during each of the first nine 
years, besides paying the $5000 to its creditors, pay into 
the sinking fund $8329. In the tenth year the process is 
reversed, and the entire $100,000 then accumulated in the 
sinking fund is taken to pay the $100,000 of "principal." 
Hence, as apphed to bonded debts, the sinking fund may be 
defined as formed by accumulating an annual sum during 
a specified period, such that its amount will just suffice 
to extinguish a given sum at the end of that period. 



Depreciation and sinking funds are not the only devices 
by which uneven income streams may be, as it were, 
smoothed out. Many other devices may be employed. For 
instance, a person engaging in an unusual expense, such as 
that of building a house, will not allow this expense to 
seriously interrupt the even flow of his income, but will 
provide for it by some correspondingly unusual item of in- 
come. He may sell other property, for instance railway 
shares; the unusual simi he realizes on the sale will then 
offset the unusual outgo for the dwelling. Or, he may 
mortgage his dwelling and the land on which it stands, 
and pay the debt off gradually — sell a claim upon the 



Sec. 8] EAENINGS AND INCOME 245 

dwelling itself instead of selling some property distinct 
from the dwelling. Or again, he may make an ar- 
rangement at the outset to pay for the house in install- 
ments. 

All of these methods of maintaining more or less regu- 
larity of income merely shift the burden of an unusual 
expense from one person to another. The first method, 
by which the purchaser of the house raises the necessary 
money by selling other property, shifts to the buyer of 
that property an expense equal to that which he himself 
seeks, for the time, to avoid. The second method, that of 
mortgage, presupposes a money lender who is ready to sup- 
ply the necessary funds. The money lender is in this case 
the one who, for the time, shoulders the burden. The 
third method, payment by installment, implies that the 
builder (or some other party) advances the cost of the dwell- 
ing. In other words, the person who attempts to smooth 
out his own income does so by throwing his irregularities 
on some one else, usually a banker or broker. 

To society as a whole such purely shifting devices are 
inapplicable, for society can find no outside party on whom 
to shift the fluctuations. There is, however, a method by 
which society's income may be more or less standardized. 
This is by assorting and combining the various instru- 
ments of capital wealth so that the various income 
streams may mutually compensate. For instance, if a 
community owns iron mines, it has a form of property 
which, for a time, probably yields more than the standard 
income. By the nature of the case, every bucketful of ore 
reduces the amount which the mine can yield in future. 
The mine is, in fact, a sort of terminable annuity. After it 
is exhausted there will be no further returns. The capital- 
value of the mine will therefore continually decrease. On 
the other hand, forest land which is covered with young 
saplings will not begin to yield much income for many 
years. The income from this capital is therefore tempo- 



246 NATURE OF CAPITAL AND INCOME [Chap. XIV" 

rarily below the standard. A community which owns both 
mine and timber land will consequently find that the in- 
crease and decrease will offset each other, so that its income 
will be more nearly standard than if it merely possessed 
either one without the other. 



The last-named method is applied to the case of capital 
which consists of a large number of instruments in differ- 
ent stages of production or consumption. If a weaving 
mill is equipped with 20 looms of the same degree of wear, 
the value of this plant will evidently depreciate and a de- 
preciation fund may be necessary. But if the 20 looms are 
evenly distributed throughout the different stages of wear, 
and if, for convenience, we assume that one loom wears- 




Fig. y. 

out each year, no depreciation fund will be necessary. The 
replacement of one loom annually is equivalent to such a. 
depreciation fund, and the capital is thereby maintained at 
a constant level. 

Any income stream whatever, even if its component 
parts are very irregular, will, if these parts are renewed at 
frequent and regular intervals, necessarily produce in total 
a uniform or standard income. Let ABC (Figure 9) repre- 
sent an income stream which at first is negative and after- 
ward positive, such, for instance, as is occasioned by first 
constructing and then using a machine. Let an exactly 
similar income stream A'B'C begin a short time later, as 
at A' , and so on indefinitely, at equal intervals. It is evi- 
dent that after we have reached the point C at which our 
first income stream ends, we have a fairly uniform income 



Sec. 9] EARNINGS AND INCOME 247 

and outgo, the income at any point consisting of the sum 
of the ordinates above the base Kne AC^, and the outgo 
of the sum of the ordinates below. 

This case brings into juxtaposition two different points 
of view from which the interest on capital may be con- 
sidered. Professor J. B. Clark conceives of interest 
as the net difference between the rate of total income 
and rate of total outgo at any point, and compares 
this net return with the capital-value as it exists at that 
point. This concept treats the outgo or cost of production 
as simultaneous with the income, that is, it takes into con- 
sideration any small section of the curves in Figure 9 
contained between any tv/o vertical lines a short interval 
apart. Professor Bohm-Bawerk, on the other hand, always 
thinks of cost of production as preceding income. He 
fixes his attention on the elementary income stream ABC, 
and contrasts the outgo or cost between A and B with the 
later income between B and C. These two points of view 
are evidently quite reconcilable, though their authors do 
not seem to have realized the fact. Each carries his own 
special point of view throughout his treatment of capital 
and interest. Professor Bohm-Bawerk regards interest as 
an agio, or premium, found by contrasting the positive in- 
come return between B and C with the investment or outgo 
between A and B, whereas Professor Clark regards interest 
as the ratio between a perpetual, uniform flow of income and 
the capital-value of the entire stock. In short, Bohm- 
Bawerk has in mind what we have called in the previ- 
ous chapter the premium concept of interest, and Clark, 
the price concept of interest. 

§10 

We have seen that earned income is often only an ideal 
standard, and not to be confused with actually realized in- 
come. Yet the confusion is common. Even Edwin Can- 



248 NATURE OF CAPITAL AND INCOME [Chap. XIV 

nan, who is usually a safe guide, makes an error at this 
point. He states in his Elementary Political Economy : ^ — 

"If a man has a cellar of port wine, or a plantation of trees, the 
annual increment of the value of these things is evidently part of his 
annual income. If he likes to spend it, he can do so without decreasing 
his property. If he does not choose to spend it, he is engaged in a 
form of saving and is thereby adding to his property." 

And again, in ''What is Capital?"^ he states, "The in- 
come is divided into two parts, (1) the increase of the 
capital, and (2) the things enjoyed." 
f> That "saving" or increase of capital is no^ income co- 
ordinately with ordinary income is evident from the fact 
that this item is never discounted in making up capital- 
value. As we have seen, one of the fundamental charac- 
teristics of income is that it is the desirable event which 
occurs by means of wealth, and for the sake of which, con- 
sequently, that wealth is valued. This definition implies 
that every item of income is discounted in order to obtain 
its contribution to capital-value. The mere increase or de- 
crease of capital-value, on the other hand, is never thus 
discounted. Suppose, for instance, with interest at 4 per 
cent, that a man buys an annuity of $4 a year, which 
does not begin at once but is deferred one year. Since 
this annuity will be worth $100 one year hence, its present 
value will be about $96, which, during the ensuing year, 
will gradually increase to $100. If this increase of value 
of (about) $4 is itself to be called income, it should be 
treated like every other item of income, and should be dis- 
counted. But this is absurd. The discounted value of $4 
would be $3.85, which, if added to the $96, would require 
that the entire value of the property to-day should be 
$99.85, or practically the same as a year later instead of 
$4 less as is actually the case. In other words, the hy- 
pothesis which counts an increase of value as income is 
self-destructive; for if the increment is income, it must 

* p. 59. 2 Economic Journal, Vol. VII, 1897, p. 284. 



Sec. 11] EARNINGS AND INCOME 249 

be discounted, but, if discounted, it is practically abolished. 
Clearly, then, increase of capital is not income in the sense 
that it can be discounted in addition to other items of in- 
come. If it is income at all, it is income in a very peculiar 
sense, and nothing but confusion can result from having 
to consider two kinds of income so widely divergent that 
whereas one is discounted to obtain capital- value, the other 
is not. / — ' 

We have seen that the increase of capital is at the ex- 
pense of income. It is occasioned by and is equal to 
the deficiency of reahzed compared with standard income. 
With this in mind, Edwin Cannan's definition of income 
could be stated as realized income plus the deficiency be- 
tween realized and earned income. But this is earned 
income, not realized, income. 

§ 11 

To put the matter in a practical light, let us imagine the 
case of three brothers, each of whom inherits the same 
fortune, say, $10,000. Let us assume that interest is 5 per 
cent. The first brother invests his $10,000 in an annual 
annuity of $500 a year forever. The second puts his in 
trust to accumulate at 5 per cent for fourteen years, at 
which time, having doubled in value, it is to be invested 
in a perpetual annuity of $1000 a year. The third, being 
of the spendthrift type, buys an annuity of $2000 a year for 
(nearly) six years. 

According to the theory here advocated, the first has 
a perpetual income of $500 a year; the second has no 
income for 14 years, and thereafter an income of $1000; 
the third has an income of $2000 a year for 6 years and 
thereafter none at all. This mode of viewing the matter 
also squares with ordinary business reckoning. 

On the other hand, according to the theory which re- 
gards increase of capital as income, although the income 
from the first would be the same as we have reckoned it, 



250 NATUKE OF CAPITAL AND INCOME [Chap. XIV 

that of the second and third would be quite different : the 
income of the second would be $500 the first year, for during 
that year his capital increases from S10,000 to $10,500; 
it would be $525 the second year, during which his capi- 
tal increases again from $10,500 to $11,025, and so on, 
imtil in 15 years he is receiving an income of $1000 a year. 
The third brother, during the first year, uses $2000; but 
as his interest is only $500 he is forced to take $1500 out of 
capital. This is, in our view, true realized income. But ac- 
cording to the theory which we are criticising, this deprecia- 
tion of $1500 would have to be deducted from the $2000 
which the spendthrift actually enjoys, in order to compute 
his net income. The net income would thus be only $500, 
or the interest on his original capital. At the beginning 
of the second year, this spendthrift brother would possess 
a capital of $8500, the ''income" of which would, by the 
same theory, be 5 per cent on $8500, or only $425. Follow- 
ing similar reasoning to the end we find that the so-called 
"income" would progressively diminish until, in the sixth 
year, it would be only $90. The capital then having been 
entirely destroyed, no income would remain. It would ap- 
pear from all this that the spendthrift had received from 
the original $10,000, during the six years of its hfe, a very 
small income, steadily diminishing from $500 to zero, the 
simi total being only $1695. Was it for such an ''income" 
that he invested $10,000 ? 

§12 

If we suppose an income tax laid on the three brothers, we 
shall find that, according to the different interpretations 
which we give to the term "income," the results will 
be startlingly different. If the income be taken in its true 
sense, namely, as those items whose capital-value is the 
$10,000 with which the three brothers started, then an in- 
come tax of 10 per cent will yield from the first brother 
^50 a year; from the second, nothing for 14 years, after 



Sec. 12] 



EARNINGS AND INCOME 



251 



which it will yield $100 a year ; and from the third, 
a year for 6 years ^ and nothing thereafter. The burden 
of the three taxes on these three brothers will under these 
conditions be exactly equal, when the three are compared 
by means of their present values. Each brother could 
''compound" for his taxes (that is, could pay a fixed sum 
in advance in lieu of the annual sums) at the same cost, 
namely, SIOOO ; for SIOOO is the sum in present cash which 
is equivalent respectively to $50 a year forever ; to $100 a 
year beginning 14 years hence; and to $200 a year for 6 
years. But turning now to the spurious interpretation of 
income as the value of uses plus the accumulation of capi- 
tal, or the value of uses less the depreciation of capital, we 
find that the three brothers would be very unequally taxed. 
The first would, as before, pay $50 a year indefinitely. 
But the second who "saves" for 14 years, will be compelled 
Second Brother 



Capital 



So-called 
" Income " 



Tax 

Thekeon 



True 

Income 



Tax 

Thereon 



At beginning 
In 1 year 

In 2 years . 

In 3 years . 

In 4 years . 

In 5 years . 

In 6 years . 

In 7 years . 

In 8 years . 

In 9 years . 

In 10 years . 

In 11 years . 

In 12 years . 

In 13 years . 

In 14 years . 

In 14^ years . 

Thereafter . 



$10,000 
10,500 
11,025 
11,576 
12,155 
12,763 
13,401 
14,071 
14,775 
15,513 
16,289 
17,103 
17,959 
18,856 
19,799 
20,000 
20,000 



525 
551 
579 
608 
638 
670 
704 
738 
776 
816 
856 
897 
943 

1000 



$50.00 
52.50 
55.10 
57.90 
60.80 
63.80 
67.00 
70.40 
73.80 
77.60 
81.60 
85.60 
89.70 
94.30 

100.00 



nil 
nil 
nil 
nil 
nil 
nil 
nil 
nil 
nil 
nil 
nil 
nil 
nil 
nil 
nil 
$1000 



nil 
nil 
nil 
nil 
nil 
nil 
nil 
nil 
nil 
nil 
nil 
nil 
nil 
nil 
nil 
$100 



* Or, to be exact, $200 a year for 5 years and $180 in the last year, 
inasmuch as the capital will be exhausted in a little less than 6 years. 



252 



NATURE OF CAPITAL AND INCOME [Chap. XIV 



to pay an annually increasing tax on this saving for the 14 
years of postponement, and then a tax on the income from 
these same savings in which his annuity is to consist. 
His first year's savings will be $500 and will be taxed $50. 
During the second year his capital grows from $10,500 to 
$11,025, making an increase of $525, the tax on which is 
$52.50, and so on, as shown in the precedmg table. 

The third brother, under such a tax, will fare as shown 
below : — 

Third Brother 



Capital 



So-called 
"Income" 



Tax 

Theeeoit 



True 
Income 



Tax 

Theeeon 



At beginning 
In 1 year 

In 2 years . 

In 3 years . 

In 4 years . 

In 5 years . 

In 6 years . 

Thereafter . 



$10,000 
8,500 
6,930 
5,270 
3,530 
1,710 
nil 
nil 



$500 
425 
340 
260 
180 
90 
nil 



$50.00 
42.50 
34.00 
26.00 
18.00 
9.00 
nil 



$2,000 
2,000 
2,000 
2,000 
2,000 
1,800 
nil 



200 
200 
200 
200 
180 
nU 



When we compare the burden of the various taxes im- 
posed on so-called "income," we shall find that the first 
brother could "compound" for his taxes, as before, by a 
cash payment of $1000. The second brother, however, 
would need to pay $1714. For he would have to pay $1000 
as the present value of the tax of $100 a year beginning in 
14 years, and in addition, $714 as the present value of 
the series of taxes on his savings, namely, $50, $52.50, etc. 
And the third brother, though the least provident of all, 
could compound for only $157.73, this being the present 
value of the six small tax payments which he would have 
to make, namely, $50, $42.50, $34, $26, $18, and $9.^ 

^ In the foregoing calculation it was assumed that the tax did not 
itself affect the value of the "income" on which the tax is laid. But 
this would be untrue of "income" which includes the increment of 
capital. For the discussion of this point, see Appendix to Chap. 
XIV, § 2. 



Sec. 13] EARNINGS AND INCOME 253 

Instead, therefore, of having a burden of taxes on the three 
brothers, all of which have an equal present value of $1000, 
we find the unequal burdens of $1000, $1714, and $157.73. 
Such a system of taxation is clearly unjust and discour- 
ages the saver, while it encourages the spendthrift. The 
spendthrift virtually has some of his taxes remitted to him, 
whereas the saver is made the victim of that too frequent 
concomitant of fallacious economic theory, — double taxa- 
tion ; for he is first taxed 15 years on his accumulation of 
capital ($10,000 in all), and thereafter is taxed again on 
the income which he derives from that same accumulation. 
And yet this procedure is very common in practice. It 
amounts to taxing, not the income actually flowing from 
capital, but its "earnings" or the interest upon the cap- 
ital. It is famihar in the "general property tax" in 
the United States. Under it such wealth as temporarily 
unproductive land is taxed, though it bears no income ex- 
cept the purely constructive income of its annual rise in 
value. To some extent also the British income tax is an 
instance of the same fallacy. 

§ 13 

In the example which has been given we have supposed 
each brother to be possessed of a fixed and definite annuity. 
We have considered the effect of an income tax on these 
properties, according to the incorrect interpretation of 
"income." It often if not usually happens, however, that 
the owner of a property may use it in any one of many ways, 
and thus derive from it any one of many income streams. 
We have seen in the previous chapter that the choice be- 
tween the different methods of using the property will de- 
pend on the question. Which source of income possesses the 
greatest present value? An income tax laid according to 
the correct idea of income would not disturb the com- 
parative merits of these different income streams; but if 
income be interpreted to include savings, the tax would 



254 NATURE OF CAPITAL AND INCOME [Chap. XIV 

disturb them greatly. The effect of such a tax as was 
illustrated in the example of the three brothers would be to 
discourage the uses of capital which involve waiting. In 
fact, this discouraging effect is well recognized and ap- 
plauded by the single-tax advocates, although they over- 
look the inequities involved. According to them, it is 
right to discourage waiting, and no speculation in real estate 
such as was described in a previous chapter should be per- 
mitted. They would tax all increase of value of land in the 
manner just described. Perhaps the most harmful case of 
such a system of taxation is that of forest land. Forestry 
advocates have long been aware of the baleful effect of the 
taxation of growing forests, producing, as it does, wasteful 
and premature cutting, and have attempted to secure a 
reduction or remission of such taxes. But the persistent 
belief that the annual increment of value of such forests is 
income and should be taxed has hitherto prevailed in 
America, with the natural consequence that the owners of 
these forests have cut them when they should have allowed 
them to grow. In Europe, a longer experience in forestry 
has led, in some cases, to a more rational system. " Baden 
exempts newly established forests from tax for twenty 
years (law of 1886). In Austria they are exempt for 
twenty-five years (law of 1869). In France three-fourths 
of the land tax is remitted for thirty years." ^ Even a 
small tax, when laid on forest land which will yield no 
timber for fifty years, becomes a very serious drain in the 
long run.^ 

§14 

The fallacy which has been exposed is not only a con- 
fusion between realized and earned income; it is also a 
confusion between income and capital. To regard "sav- 

1 " How shall Forests be Taxed? " by Alfred Gaskill, Forestry and 
Irrigation, April, 1906, p. 173. 

^ Some limitations on the applications of a theoretically correct in- 
come tax are mentioned in the Appendix to Chap. XIV, § 3. 



Sec. 14] EARNINGS AND INCOME 255 

ings" as income, is essentially to regard an increase of 
capital as income. But from what has been said it is clear 
that he who increases his income must decrease his capital 
to an equal extent. / Capital and income are thus mutually- 
exclusive. One cannot receive the whole standard income, 
and at the same time secure also an increase of his capital. -'i^^ 
The truth of this has been instinctively expressed in the 
adage, "You cannot eat your cake and have it too." 
O We have learned, then, to distinguish between standard 
and realized income. The one is ideal, the other actual. 
Tiie one is that income which, if it were received, would 
leave the level of capital- value unchanged ; the other is that 
income which is actually received and detached from capi- 
tal, no matter whether that capital, as a result, is increased 
or decreased. In short, the one is earned, the other realized. 
The two may, of course, coincide, in which case capital- 
value remains constant. When they do not coincide, the 
discrepancy measures the increase or decrease of capital- 
value. This discrepancy may be partially or wholly done 
away with by means of a depreciation fund or other de- 
vices whereby realized income, otherwise irregular, is made 
regular. But, merely to reckon depreciation is not to pro- 
vide for it. It merely stigmatizes part of realized income 
as "coming out of capital," but it does not make good 
the loss of capital nor prevent its becoming a part of 
realized income. No more does the mere calling of "sav- * 
ings" by the name of income make it reaHzed as income J\_ 
These two procedin-es are both attempts to standardize 
income in thought when it is not standardized in fact. 
We have seen that they represent a confusion both be- 
tween capital and income and between income which is 
merely earned and income which is actually realized, and 
that they lead to inequitable taxation — double taxation 
to the saver and remission of taxes to the spendthrift. 



CHAPTER XV 

CAPITAL AND INCOME ACCOUNTS 
§ 1 

The last two chapters have their counterpart in accomit- 
ing. Correctly kept accounts will show that an abnormal 
increase of income is always at the expense of capital. In 
the case of a corporation, the distribution among the stock- 
holders of such excessive income is called ''paying divi- 
dends out of capital." It is not necessarily or always 
wrong. A Land Company of California has already been 
cited as a legitimate case. A case at the opposite ex- 
treme would be one in which the dividends are made 
unusually small in order that the capital may be in- 
creased. There is in New York City a company which 
has never declared any dividends, but has been rolling up 
a large surplus for years, and whose stock is for this reason 
much above par. 

We have already seen in Chapter VIII, that every item 
in an income account represents the income or outgo from 
some item in the capital account. That is, the income ac- 
count consists merely in a statement of the income and 
outgo connected with each item of asset or liability, includ- 
ing that class of assets and liabilities which are alike claims 
and obligations, such as leases and employees' contracts. 
If the income for each item remains steady or standard, the 
relation between the capital and income accounts is very 
simple. In such a case (supposing the rate of interest to 
be 5 per cent), each item in the capital account will con- 
stantly stand at twenty times the amount of the corre- 

256 



Sec. 2] CAPITAL AND INCOME ACCOUNTS 257 

spending item in the income account. Let us suppose a 
factory company operating a plant worth $300,000, which 
is bonded for $100,000. The remainder, $200,000, will 
represent the capital and surplus of the company If these 
valuations represent a true and not simply a fictitious book 
value, and if the rate of interest be taken at 5 per cent, the 
fact that the plant is worth $300,000 signifies simply that 
its earning power is $15,000 a year, of which $5000 goes 
in interest to the bondholders and $10,000 in dividends 
to the stockholders. The capital and income accounts of 
such a firm, doing a steady and uninterrupted business, 
would repeat themselves in monotonous regularity year 
after year. 



If now we suppose that the repairs and replacement of 
the plant do not occur in equal amounts each year, but that 
it is necessary, at long intervals, to make large, special, or 
extraordinary repairs ; there will occur during the interme- 
diate years "depreciations" of the plant, and sudden res- 
torations in its value when these special repairs are made. 
Thus, suppose that during the year 1900, the factory 
depreciates by $10,000. The capital account at the begin- 
ning and end of this year, and the income account during 
the year, will be given in the following table : — 

Capital Account at Beginning op Year 1900 

Assets Liabilities 

Factory $300,000 Bonds $100,000 

Capital and surplus . 200,000 

$300,000 $300,000 

Capital Account at End op Year 1900 

Assets Liabilities 

Factory $290,000 Bonds $100,000 

Capital and surplus . 190,000 

$290,000 $290,000 



258 NATURE OF CAPITAL AND INCOME [Chap. XV 

Income Account during Year 1900 
Capital Source Income Outgo Net 

Factory Product . $40,000 Running ex- 

penses . . $15,000 + $25,000 
Bonds Interest . . 5,000 - 5,000 

Capital and 

Surplus Dividends . 20,000 - 20,000 

$40,000 $40,000 000 

From this table we see that the factory 5delds $25,000; 
as it is worth only $300,000 (on a 5 per cent basis), by the 
principles of Chapter XIV, it cannot yield more than 
$15,000 without depreciating to the extent of the dif- 
ference ($10,000); but, instead of setting aside something 
for depreciation, i.e. to pay for future repairs, the com- 
pany has declared larger dividends. Hence, corre- 
sponding to the depreciation of $10,000 in the value of the 
plant there is an excess of $10,000 above the "standard" 
income received by the stockholders. Instead of $10,000, 
which is the normal interest on their capital and surplus of 
$200,000, they receive $20,000. The extra $10,000 above 
the standard thus corresponds precisely to the depreciation 
of their property, which accordingly sinks in the course 
of the year from $200,000 to $190,000. 

During the next year we shall suppose that the factory 
yields again $25,000. Since its value was, at the beginning 
of the year, $290,000, it cannot, on a 5 per cent basis, yield 
more than $14,500 without depreciating to the extent of 
the difference (in this case $25,000-$ 14,500, or $10,500). 
Its value at the end of the year exclusive of improvements 
is consequently $290,000 -$10,500, or $279,500. We shall 
suppose that the entire depreciation for the two years, 
$20,500, is made good by extraordinary repairs to that 
amount. Since the factory yields only $25,000 and only 
$20,000 after the bondholders are paid, it will be necessary, 
in order to meet the $20,500 of repairs to assess the stock- 
holders $500. The accounts will then stand as follows : — 



Sec. 3] 



CAPITAL AND INCOME ACCOUNTS 



259 



Capital Account at Beginning of Year 1901 
Assets Liabilities 

Factory S290,000 Bonds 

Capital and surplus . 



$290,000 



$100,000 
190,000 

$290,000 



Capital Account at End of Year 1901 
Assets Liabilities 

Factory $300,000 Bonds 

Capital and surplus . 



$300,000 

Income Account during Year 1901 
Capital Source Income Outgo 

Factory Product . $40,000 Running ex- 
penses . . $15,000 
Special repairs . 20,500 
Bonds Interest . . 5,000 

Capital and 

surplus Assessment 500 Dividends . . 000 



$100,000 
200,000 

$300,000 



Net 

+ $4500 
-5000 

+ 500 



$45,500 



$45,500 



000 



§ 3 



Had the repair bill been distributed over the two years, 
the dividends to the stockholders, instead of being S20,000 
the first year and less than nothing the second, would have 
been $10,000 in each. In order to make their income thus 
stable and "standard" instead of irregular, it is only neces- 
sary to employ a special repair fund. This accumulates for 
a few years as a separate investment, and is then con- 
verted back into the plant itself, which meanwhile will 
have continued its depreciation. We shall assume that this 
plan is adopted, beginning with the year 1902, for which the 
capital and income accounts will be as follows : — 

Capital Account at Beginning op Year 1902 
Assets Liabilities 

Factory $300,000 Bonds $100,000 

Capital and surplus . 200,000 



$300,000 



$300,000 



260 NATURE OF CAPITAL AND INCOME [Chap. XV 

Capital Account at End of Year 1902 
Assets Ldabilities 



Factory $290,000 


Bonds 


$100,000 


Eepairfund .... 10,000 


Capital and surplus . 


200,000 


$300,000 




$300,000 


Income Account during Year 1902 




Capital Source Income 


Outgo 


Net 


Factory Product . $40,000 


Running ex- 






penses . . $15,000 


+ $25,000 


Repair fund 


Investment . 10,000 


- 10,000 


Bonds 


Interest . . 5,000 


- 5,000 


Capital and 






surplus 


Dividends . 10,000 


- 10,000 



$40,000 $40,000 000 

Here we see that the value of the plant depreciates by 
$10,000 as before, but that, to replace the loss, there are 
$10,000 worth of repair funds invested in, say, stocks and 
bonds. The consequence of the repair fund is that the value 
of the assets of the company remains stationary at $300,000 ; 
the share of this property which falls to the stockholders 
also remains at a constant level, namely, $200,000; and 
the stockholders receive dividends of only $10,000 instead 
of $20,000, having set aside $10,000 to invest in their 
repair fund. We may suppose that during the next year 
the depreciation continues and that the factory yields again 
$ 25,000, as we saw in § 2. Since its value was only $ 290,000, 
the ''earnings" of which are only $14,500, it must have 
depreciated $ 10,500. Since the repair fund set aside in the 
previous year has earned 5 per cent, or $500, the accounts 
for the year 1903 will now be as follows : — 

Capital Account at Beginning op Year 1903 

Assets Liabilities 

Factory $290,000 Bonds $100,000 

Repair fund .... 10,000 Capital and surplus . 200,000 

$300,000 $300,000 



Sec. 3] 



CAPITAL AND INCOME ACCOUNTS 



261 



Capital Account at End of Year 1903 

Assets Liabilities 

Factory $279,500 Bonds $100,000 

Repair fund .... 20,500 Capital and surplus . 200,000 

$300,000 $300,000 

Income Account during Year 1903 

Capital Source Income Outgo Net 

Factory Product . $40,000 Running 

expenses $15,000 + $25,000 
Repair fund Interest New invest- 

received 500 ment . 10,000 1 





Interest re- 


\ 


- 10,000 




invested . 


500 J 




Bonds 


Interest 


5,000 


- 5,000 


Capital and 








surplus 


Dividends 


10,000 


- 10,000 



$40,500 



$40,500 



000 



Here we see that the repair fund has absorbed in outgo 
another $10,000 of new investment, and that it has yielded 
an income of $500, which, however, has been immediately 
reinvested and appears as outgo also. The consequence is 
that in the capital account at the end of the year, the factory, 
which has depreciated now to $279,500, has, synchronously 
with its depreciation, acquired a repair fund enough to 
bring up the total value of the assets to $300,000. The 
value to the stockholders, therefore, remains stationary at 
$200,000, on which amount they have received their stand- 
ard income of $10,000. 

§4 

During the next year, we shall suppose, the extraor- 
dinary repairs again need to be made. Inasmuch as during 
this year the plant has continued to depreciate, the special 
repairs will amount, approximately, to $31,500, whereupon 
the repair fund is sold and the cash employed in actual 
repairs. The accounts for the year 1904 will then be as 
-follows : — 



262 



NATURE OF CAPITAL AND INCOME [Chap. XV 



Capital Account at Beginning op Year 1904 
A sse is Liabilities 



Factory $279,500 Bonds 

Repair fund . . . 20,500 Capital and surplus . 

$300,000 

Capital Account at End of Year 1904 
Assets Liabilities 

Factory (exclusive of 



$100,000 
200,000 

$300,000 



impro vemen ^s"! 


$268,500 
31,500 


Bonds 




$100,000 


Improvements 


3 , , , 


Capital and 


surplus . 


200,000 


Repair fund , 


■ ■ ■ 


000 










$300,000 


$300,000 




Income Account during Year 


1904 




Capital Source 




Income 




Outgo 


Net 


Factory 


Product . 


$40,000 


Running 
expenses 


$15,000 










Special re- 


31,500 J 


-$6,500 








pairs 




Repair fund 


Sale of 
entire 
fund in 




New in- 
vest- 








Dec. . 


31,500 


ment 


10,000 ( 


+ 21,500 




Interest . 


1,000 


Interest 


1,000 i 


Bonds 






Interest 


5,000 


- 5,000 


Capital and 












surplus 






Dividends . 


10,000 


- 10,000 



$72,500 



$72,500 



000 



Here we see that during the year 1904, the value of the 
factory at the beginning was $279,500, and at the end, 
exclusive of improvements, $268,500. But the improvements 
or special repairs amounting to $31,500 have made up the 
total value of the factory to $300,000. There is at this time 
no repair fund whatever, as it has all been absorbed in 
improving the factory. The assets, therefore, amount to 
$300,000; the property of the stockholders remains sta- 
tionary as before at $200,000; and their dividends also 
remain stationary at $10,000. The factory itself during this 



Sec. 5] CAPITAL AND INCOME ACCOUNTS 263 

year does not yield the S25,000 which has regularly ap- 
peared as the net income in the previous accounts, for during 
tliis year we have to charge to the factory the special repairs 
of $31,500. The factory itself, therefore, produces a net 
deficit of $6500, offset by the large proceeds received from 
the sale of the repair fund of $31,500, which, less the new 
investment of $10,000 during the year, shows a net return 
for the year of $21,500. We see, therefore, that the exist- 
ence of the repair fund to cover depreciation virtually 
maintains the capital accounts at a constant level, merely 
changing from year to year the form of the items, but not 
affecting either the interest of the bondholders or the 
dividends of the stockholders. In other words, the repair 
fund acts as a means of standardizing the stockholders' 
income. In ordinary business accounting, such standard- 
izing is regarded as sound poHcy. 

§5 

Certain exceptions occur, as in the case of mining com- 
panies or land companies which necessarily must terminate 
their operations in the more or less remote future. But 
even in such instances, the instinct of the accountant 
toward standard accounting is so strong, that he usually 
treats the excess or deficiency of real income with relation 
to standard income in a special manner. 

Thus, when a company winds up business, the final dis- 
tribution of the proceeds is not treated as an ordinary 
dividend; the most of these proceeds are regarded as 
capital returned to the stockholders. The "company" 
therefore goes through the form of paying for the shares 
of its stockholders and enters what it thus pays over to the 
stockholders as a cost of purchase instead of as a dividend. 

The reverse operations may occur if at any time the stock- 
holders forego their dividends. It is in such a way that a 
company usually enlarges its capital. It nominally dis- 
tributes the regular dividends, but allows the stockholders 



264 NATURE OF CAPITAL AND INCOME [Chap. XV 

who choose to do so to reinvest them and receive in return 
new stock certificates. 

§6 

From the foregoing accounts it is clear that the theory 
of capital and income which has been explained appUes 
practically to the accounting ordinarily employed in busi- 
ness. Such accounting is, in fact, nothing but a method of 
recording the items of income and their capitalization at 
different points of time. A merchant's balance sheet is a 
statement of the prospects of his business. Each item in it 
represents the discounted value of items which he may 
expect later to enter in his income account. Rightly in- 
terpreted, the capital account merely represents as a whole- 
the capitalization of expected items in the income account ; 
the fluctuations of the capital account correspond with the 
deviations from the standard income in the items of the income 
account; and where there are no such fluctuations, every 
item of the income account is equal to the standard income 
from the corresponding items of the capital account. 

There are, of course, numerous practical modifica- 
tions of this general statement to be made when actual 
accounts are treated. It was shown in Chapter VIII that 
such modifications are due to a variety of circumstances, 
such, for instance, as the influence of that important ele- 
ment, risk; the desire of accountants to maintain their 
capital accounts unchanged from year to year; and the 
omission from their capital accounts of such two-sided 
items as leases, employee-contracts, and the like. But none 
of the exigencies of practice militate in the least against our 
theory of capital and income accounts. In all cases the 
income account simply records the values of the services 
and disservices of articles of property through any given 
period ; and the capital account records the present values 
of those articles, as resulting at any given instant from the 
expected values of their services and disservices. 



CHAPTER XVI 

THE RISK ELEMENT 



Throughout the three previous chapters, we have as- 
sumed the existence of artificially simple conditions. We 
have assumed that the entire future history of the capital 
in question is definitely known in advance ; in other words, 
we have ignored chance. The factory which was taken 
for illustration was supposed to yield definite future in- 
come which could be counted upon as a bondholder counts 
upon his interest. In actual practice, however, every factory 
or other enterprise offers chances both of gain and loss. 
How these chances affect capital-value will be discussed 
in the present chapter. 

We have seen that capital-value increases as an antici- 
pated installment of income approaches in time, and 
diminishes as that installment is reached and passed. These 
changes in capital-value take place when the future in- 
come is regarded as certain. The introduction of the 
element of chance will bring other and even more impor- 
tant changes in capital-value. If we take the history of 
the prices of stocks and bonds, we shall find it chiefly to 
consist of a record of changing estimates of futurity, due 
to what is called chance, rather than of a record of the 
foreknown approach and detachment of income. Few, if 
any, future events are entirely free from uncertainty. In 
fact, property, by its very definition, is simply the right to 
the chance of future' services. A mine owner takes his 
chances as to what the mine will yield; the owner of an 
orange plantation in Florida takes risks of winter frosts; 

265 



266 NATURE OF CAPITAL AND INCOME [Chap. XVI 

the owner of a farm takes risks as to the effect of sun 
and rain and other meteorological conditions, as well as 
risks of the ravages of fire, insects, and other pests. In 
buying an overcoat a man takes some risk as to its effec- 
tiveness in excluding cold, and as to the length of time it 
will continue to be serviceable. Even what are called 
"gilt-edged" securities are not entirely free from risk. In 
a sense, therefore, every owner of property is a risk-taker. 
Some persons will estimate more highly than others the 
risks taken. From this fact it might seem that there 
is a distinction between the actual risk incurred and the 
estimate which individuals put upon it. But a little 
consideration will show that this distinction is spurious; 
for, by the nature of the case, chance is always an estimate. 
Chance is subjective. Although one man's estimate may 
be better than another's through superior knowledge, intui- 
tion, or experience, the best estimate is still only an estimate, 
not a certainty. In the actual world of events there is no 
uncertainty. Aside from human opinion, there is no such 
thing as chance. To an omniscient being, all things are 
certain. 

It must be admitted that this view of chance is not 
familiar to the ordinary man, nor is it universally accepted 
by the professed students of chance. Thus, writers like 
Dr. Venn, adhering to an objective theory, regard the chance 
of an event as the number of times it would occur in the 
long run, out of the total series of possible occurrences. But 
no matter how long the "run," the number of times the 
event actually occurs seldom corresponds exactly with the 
chance of its occurring. Even in so simple a case as coin- 
tossing, 1000 trials will not often give exactly 500 heads 
and 500 tails. Yet even the " long-run " theorists regard 
the chances of heads and tails as even. If 600 heads fall 
and only .400 tails, the odds are not 6 to 4. To this objec- 
tion the only answer offered by the long-run theorists is 
that the run is not long enough, that heads and tails are 



Sec. 1] THE RISK ELEMENT 267 

equally probable because the longer the trial is continued 
the more will the two tend toward equality. But they 
argue in a circle. It is not necessarily true that the 
longer the run the more closely will the frequency of the 
event approach its probability. For example, it is possible 
that though heads and tails have an equal chance, a run 
of heads may keep up for any given number of times, 
however long, a million, for instance; or that at first heads 
and tails may occur with equal frequency and as the ex- 
periment proceeds they may diverge more and more from 
such equality. No student of chance, whatever his theory 
of the philosophy of chance, would claim that these cases 
are impossible. The most that can be said is that they are 
extremely improbable. The statement, therefore, that the 
longer the run the more closely will the frequency of the 
event approach its probability turns out to be ''the longer 
the run the more probably will the frequency correspond 
to the probability." This is true as a proposition and it is 
in fact known as "BernoulU's Theorem"; but it cannot 
be made the basis of a sound definition of probability, for 
probability would be defined in terms of itself. It states 
that the probability of heads coming up is the frequency 
which heads will probably approximate in the long run ! 
How else than in terms of probability can we formulate 
the conditions under which in the long run the coin 
"will" fall according to its probability? It is precisely 
at this point that the radical difficulty with the "long- 
run " theory is seen. It is said that in an athletic contest, 
the chance of winning is one half when two wrestlers are 
so nearly mated that in the long run "under precisely the 
same conditions," each will win in half the contests. If 
the conditions are, Hterally speaking, precisely the same, 
then the same result will necessarily follow and the same 
man will always win. It is only as the conditions vary 
slightly from time to time in their unknown elements that 
there is a change of winner ; and the instant the unknown- 



268 NATURE OF CAPITAL AND INCOME [Chap. XVI 

ness of these elements is introduced into the problem, the 
observer unconsciously shifts his ground from the " long 
run " to the true theory of chance. 

Chance is, then, an affair of human knowledge or igno- 
rance. According to this — the ignorance — theory, chance 
is not objective, but subjective. Outside of the mind, 
chance has no place. If a man holds a coin in his hand and, 
without letting it be seen, asks his neighbor what the 
"real" chance is that heads are up, will not the latter reply 
one half ? But as a matter of fact the position of the coin 
is absolutely determinate. Either heads are up, or tails 
are up; there is no ambiguity. Without changing the 
coin, the holder opens his hand. He sees that heads are 
up. Without disclosing this fact to his neighbor he re- 
peats the question, "What is the chance that heads are 
up?" Will not the latter still reply, "One half"? To 
Mm, in his ignorance about the coin, the chances are 
exactly even; but to the man who holds the coin and 
whose eye has seen it, there is no uncertainty. He knows 
that heads are up. For him the element of chance has 
vanished because the element of ignorance has vanished. 
Chance exists only so far as ignorance exists ; varies with 
different persons according to their comparative ignorance 
of the matter under consideration ; and is in fact a measure 
of ignorance. 

Of course the actual statistical record may afford an im- 
portant and sometimes the only basis for our degree of 
knowledge and ignorance. Practically it therefore often 
happens that we derive our estimate of chances from the 
behavior of events "in the long run." It is thus that the 
chances of fire, shipwreck, and death are estimated by the 
insurance companies. But while statistics supply data 
for the forming of subjective estimates of chances, they do 
not, themselves, constitute chances; and even when they 
enter into the problem the insurance examiner does not 
follow them blindly. He always examines the special 



Sec. 2] THE RISK ELEMENT 269 

circumstances of each case; and his final estimate of the 
chance that a particular building will burn, a particular 
ship founder, or a particular person die, is based on all the 
data available, among which the data supplied by statis- 
tics are an important but by no means the sole element. 

To apply this idea of chance to an economic example, 
consider a gold mine. What is the chance that it conceals 
a rich lead of ore ? The ordinary man makes an estimate, 
based on his experience or inexperience. The geologist 
has additional knowledge and would make a different esti- 
mate. In actual fact, however, gold is either actually 
there in certain definite quantities, or is totally absent. 
It is a coin held in nature's closed hand. 

§2 

But, in showing that chance is purely a psychological 
and not an objective magnitude, we are still far from de- 
fining chance as a mathematical magnitude. In order to 
measure chance, it is necessary to state (1) when two 
chances are equal or unequal; and (2) when one chance 
bears any given ratio to the other. 

The chance of one event is said to be equal to the chance 
of another in the mind of a particular individual, when that 
individual has no inclination to beheve that one will occur 
rather than the other. One of the chances is said to exceed 
the other when the individual is "inclined to believe" 
that one event will occur rather than the other. The test 
of the equality of two chances is mere indecision of opinion 
— opinion exactly and evenly balanced. 

Next comes the question of the ratio of two chances. 
When it is said that the odds in favor of one event as 
compared with another are two to one, the meaning is 
that out of three equally probable combinations of condi- 
tions, two imply the first event and only one the second. 
Thus, if there are three cards in a hat, of which it is 
known that only one will draw a prize, the chance against 



270 NATURE OF CAPITAL AND INCOME [Chap. XVI 

a person who draws a card from the hat receiving the prize 
is two to one; for of the three equally probable drawings, 
two are blanks. 

In general terms the odds in favor of one event as com- 
pared with another are said to be m to n when there are 
m + n equally probable cases in which one or the other of 
the two events may happen, and among these m + n cases 
there are m cases such that the first event would happen, 
and n cases such that the second event would happen. 
The chance of the first event is then —^ and the chance of 
the second is ~. The m and the n cases are, it should 
be noted, assumed to be mutually exclusive.^ 

Probability is thus not merely an affair of pure mathe- 
matics, as is so often imagined. It is, first of all, a matter 
of concrete human estimate. What are called the mathe- 
matics of probability apply only to arrays of equally prob- 
able combinations, and consist in calculating the number of 
these which are favorable or unfavorable to a given event. 
The mathematics of probability never estabhsh a prob- 
abihty of itself, but always rest on some human estimate 
of chances which are equal to start with. Like every other 
branch of applied mathematics, it must depend on having 
its raw material supplied from without. By mathematics 
we seem to discover that the chance of throwing double 
sixes with two dice is one in thirty-six. But this calcula- 
tion rests on the hypothesis that, in some person's esti- 
mation, each die is equally liable to fall on any one of 
its six faces. Starting with this assumption, it is easy to 
show that in throwing two dice there are thirty-six equally 

^ It often happens that we cannot divide the field of probability 
into separate cases all equally probable. In such a case the mind is 
forced to make an estimate. For instance, the probability of an 
event may be said to be one third against the field if the estimator's 
state of opinion toward the field is exactly similar to his state of 
mind toward another field in which the division into three separate 
combinations is possible and one of them favors the event in ques- 
tion. If the state of mind is similar but less definite, then the chance 
is " about " one third but not definite. 



Sec. 3] THE RISK ELEMENT 271 

probable cases and that only one of these will give double 
sixes. Mathematics could not obtain the result unaided 
by experience. All that mathematics accomphshed with 
the dice was to derive a result from the assumed con- 
ditions of two sets of six equal chances. Whether these 
assumed conditions existed was a question, not of mathe- 
matics, but of concrete opinion. If the dice were known to 
be "loaded," the case would be materially altered. 

§3 

C'Lln order to apply this theory of chance to the valuation 
of capital, we observe that both the future rate of interest 
and the future items of income are uncertain. In the prob- 
lem of capital-valuation, however, the uncertainty in the 
rate of interest does not always enter, for only present 
and not future rates are employed at the time at which 
the valuation of the capital is made. When we call a rate 
a " present " rate we mean, of course, that the contract 
or estimate to which it relates is a present contract or 
estimate.^; The very fact of valuation implies a known 
rate or rates at which the valuer is contrasting present 
and future goods. There may be several " present " rates. 
Thus if the " present " be the year 1906, we may imagine 
a whole series of rates of interest holding true in 1906 for 
such a man ; for instance, 4 per cent for a 1-year contract, 
6 per cent for a 5-year contract, and 5 per cent for a 15- 
year contract, all originating at the present moment. All 
of these rates are fixed and known and hold true in the 
year 1906, but they do not determine the rates which 
will hold true for the contracts or estimates of 1907 or 
1914. 

In valuing capital, therefore, it is not necessary to regard 
the rate of interest as uncertain except when the rate in 
question is a future rate. 

Let us suppose that in Figure 10 the income AB is 
due at the end of the time FA, and that the rate of interest 



272 



NATURE OF CAPITAL AND INCOME [Chap. XVI 



is such as to produce the discount curve BE. Then the pres- 
ent value of AB is FE. But the future valuations of AB 
may not follow the line EB as they would were the rate 
of interest unchanged. Thus, at a midway point of time, 
G, the valuation of AB may be only GD, found by means of 
a higher rate of interest involving the steeper discount curve 
DB. The history of the value of the property, namely, 
the right to AB, therefore follows the broken line ECDB^ 
abruptly changing from GC to GD, if we suppose G to be 



--^^^=^^^^ 




F G 

Fig. 10. 

the point at which the rate of interest changes unexpectedly 
from one level to the other. Had the owner of the property 
foreseen at the start that when the point G was reached 
the rate of interest would be higher, he would have taken 
this fact into account in valuing the property at the moment 
F, and the value would have been FE% found by using the 
discount curve BDE'. This curve has a slight angle at D, 
being composed of the curve BD, constructed according to 
the high rate of interest prevailing at the time G, and the 
curve DE,' constructed according to the lower rate of in- 
terest which applies to the period FG and which was em- 
ployed in the curve EC. The essential fact, therefore, is 
that because of the failure to foresee the future rise in the 



Sec. 4] THE RISK ELEMENT 273 

rate of interest, the value of the property is FE, instead of 
FE', and that the value of the capital will fall, as at CD, 
or it may be rise, in accordance with successive future ad- 
justments in the rate of interest. Since these readjust- 
ments are usually small and gradual, fluctuations in the 
capital-value will not ordinarily be as great or as abrupt 
as here represented, but the principle involved will still 
hold true. We see, therefore, a new cause for the 
fluctuations in capital-value, namely, unforeseen changes 
in the rate of interest. 

§4 

^ There is, however, a more fundamental way in which a 
change in the rate of interest enters into our calculations, 
for it will affect the magnitude of the future income items 
themselves. In the above example it was assumed that 
the income items were not dependent on the rate of interest. 
But it often happens that the income items are not elements 
of what in Chapter VIII we called "final income," but are 
"interactions"; or, in more practical language, it often 
happens that the income is to be reinvested. In this case 
such an item cancels itself out and leaves in its place a 
series of income items in the future, and the magnitude of 
the income items in this later series will depend on the rate 
of interest at which the preliminary "interaction" was re- 
invested. If the intention in advance is to reinvest, it 
becomes important not simply to know the present rate 
of interest, but to forecast the future rate. This enters 
into the calculations of an investor who holds a 25-year 
bond at 5 per cent. He will usually regard the final pay- 
ment as "principal," intending that when it becomes due 
it shall be reinvested in a similar 25-year bond. He, there- 
fore, is not really buying a 25-year income stream of 15 
a year plus $100 at the end of the term, but is buying, let 
us say, a SO-year income stream consisting of $5 per year 
for the first 25 years and an unknown amount per year dur- 



274 NATURE OF CAPITAL AND INCOME [Chap. XVI 

ing the second 25 years. In order to forecast what income 
will be received in the second period, he has to forecast 
the rate of interest. In other words, although the bond repre- 
sents nominally a fixed and certain series of income items, 
yet, in view of the intention to reinvest, it actually repre- 
sents an income which is quite uncertain after 25 years, . 
because of the uncertainty in the future rate of interestyC. 
Such an investor, if he expected the rate of interest at the 
end of 25 years to be 2 per cent, would, in purchasing the 
above-mentioned bond, be getting %5 a year for 25 years 
and $2 a year for the next 25 years. Under these conofi- 
tions, if he could buy a 50-year bond at 4 per cent, he would 
prefer to do so. But, if he expected the rate of interest to 
remain, for each 25-year period, at 5 per cent, he would pre- 
fer, rather than invest now in a 50-year bond at 4 per cent, 
to invest in the 25-year bond at 5 per cent, intending to 
reinvest at 5 per cent at the expiration of the term. His 
forecast of what the rate of interest will be in 25 years will 
thus materially affect the choice of his investments to-day. 
Those who expect the rate of interest to fall will prefer to 
invest in long-time securities at the present market rates, 
even when those rates are less than on securities of shorter 
time, while those who expect the rate of interest to rise will 
prefer short-time securities. In the case of insurance com- 
panies which are constantly reinvesting, a change in the 
rate of interest becomes a very serious matter. One of 
the actuaries of a large company has recently pointed out 
that such changes in the rate of interest are not uncommonly 
encountered and are more important for the prosperity 
of the company than the most unusual changes in the mor- 
tality tables. Insurance companies can only roughly take 
account of the chances, reckoning that the greater the 
Hkelihood of a rise, the better the policy of making tem- 
porary investments at high rates; and the greater the 
Hkelihood of a fall, the better the policy of making 
permanent investments, even at moderately low rates. 



Sec. 5] THE RISK ELEMENT 275 

§5 

The main application of risk to capital valuation is, 
however, not to the rate of interest, but to the income 
items themselves. To this application we now address 
ourselves. Let us begin by considering the case in which 
the element of discounting is wholly absent. The simplest 
case is that of ordinary gambling. If one invests in a 
lottery ticket where there is one chance in ten of drawing 
a fyize of $50, it is evident that the price of the ticket 
must be considerably less than $50, which is the income 
it may yield. Mathematicians have called the product 
of the prize multiplied by its probability, the ''math- 
ematical value" of the chance. In the present instance 
this "mathematical value" will be $50 x -^^^ or $5. 
If a professional gambler should always pay the mathe- 
matical value of the chances, he would, in the long run, 
probably come out about even, as is well known from 
"Bernoulh's Theorem." Thus, if he continued to try for 
such $50 prizes, paying each time $5, he would probably 
win about one time in ten. In a thousand trials, there- 
fore, he might expect to win 100 times, spending $5 each 
for his 1000 tickets, or $5000, and receiving $50 each for 
his 100 prizes, or $5000. 

But the actual price which one will pay is not necessarily 
the mathematical value of the chance. It may be higher ; 
it is usually lower. The gambler is usually a person who 
will pay more than the mathematical value of the chance. 
At Monte Carlo, the "bank" makes its profit in this way, 
although its victims know full well that they are paying 
more than the mathematical value of their chances. The 
consequence, of course, is ruin to most of them. Fortu- 
nately, persons who deliberately gamble are in most com- 
munities in the minority. The ordinary man is unwilhng 
to pay even the full mathematical value of the chance. 
He is reluctant to assume any risks, and is, on the 



276 NATURE OF CAPITAL AND INCOME [Chap. XVI 

contrary, willing to make sacrifices in order to rid himself 
of them. Where the gambler would be willing to pay more 
than $5 for his lottery tickets, the cautious investor would 
only be induced to buy such tickets for considerably less 
than S5. To him, the chance of gain is outweighed by the 
prospect of loss. Rather than risk little in order to obtain 
large gains, he prefers to sacrifice much in order to avoid 
large losses. It is this sentiment which gives rise to 
the phenomenon of insurance. 

§6 

There are three values which apply to an uncertain 
return : (1) the value which that return would have if the 
uncertainty could be eliminated, or its riskless value; 
(2) the value which would be attached to it if the investor 
were willing to pay the product of the income by the chance 
of obtaining it, or the mathematical value ; (3) the value 
which he is actually willing to pay, or the commercial value. 
Thus in the case of the lottery ticket, entitling the 
holder to the chance of SlOO, the riskless value is 
$100; the mathematical value is $5; and the commer- 
cial value, more than S5 for the reckless, less for the 
man of ordinary caution, and just $5 for those of an 
intermediate temperament. 

The ratio of the mathematical to the riskless value may 
be called the " coefficient of probability." In the supposed 
case of the lottery ticket this coefficient is -^^q. The ratio 
of the commercial to the mathematical value — a ratio 
which will vary according to the temperament of the in- 
dividual — may be called the "coefficient of caution." 
In the case of a man who values his chance at $4, this coeffi- 
cient would be f . Given these ratios, we can for a given 
individual derive the commercial value from the riskless 
value by multiplying the riskless value by the coefficient 
of probability and the result by the coefficient of caution, 
thus : $ 100 X if -g- X I = $4. The product of these two ratios 



Sec. 7] THE RISK ELEMENT 277 

is the ratio of the commercial to the riskless value 
(loo"^ i= To^o) ^^'^ ™^y t>^ called the coefficient of risk} 
The coefficient of caution expresses a feature of individ- 
ual character as determined partly by nature and partly 
by environment. In times like the colonial period when 
lotteries were common, or in places like Monte Carlo, where 
gamblers congregate, the coefficient of caution is such as to 
represent an abnormal lack of caution. The opposite 
extreme is found in the timid investor who hoards money 
rather than risk its investment in any form. The coefficient 
of caution also varies with the same individual under 
different circumstances. Chief among these varying cir- 
cumstances, as Professor Norton has pointed out, is the 
amount of capital of which the individual is possessed. 
The more capital a man possesses, the less is his chance 
of serious loss in any enterprise involving risk ; and for this 
reason a rich man finds it possible to grow still richer. 
The rich can well afford to lose millions where the poor 
could barely afford to lose hundreds. There is less likeli- 
hood of ruin to the United States Steel Corporation from its 
projected investment of $75,000,000 to found a new steel- 
producing city than there would be to a workingman 
who makes a " safe " investment of $1000. 

§7 

We are now in a position to apply these principles of 
probability to the valuation of capital, i.e. to the capitaliza- 
tion of uncertain income. The most important classifica- 
tion of investments from a practical point of view is into 
two categories of safe and unsafe investments. But even 
in so-called safe investments the element of risk enters. 
As between bonds and stocks, the latter usually represent 
the precarious and the former the safe investments; yet 
in the case of bonds, the receipt of interest and principal 
is always in some degree a matter of uncertainty. 

^ For a mathematical statement, see Appendix to Chap. XVI, § 1. 



278 NATURE OF CAPITAL AND INCOME [Chap. XVI 

Take, for example, a "5 per cent" bond running for 
10 years. Let us assume that the market rate of mterest 
is 4 per cent, in the sense that $100 at any time will exchange 
for $104 certain one year later. Under these conditions, 
the bond ought to sell for $108 (see Chapter XIII). That 
is, an investor buying this bond at a premium of $8 will 
in 10 years "make" 4 per cent provided he receives all 
the sums stipulated. The $108 is the ''riskless value" 
of the bond. 

But, while $108 would be the price of the bond were the 
investor absolutely sure of the income items to which it 
entitles him, he may feel that there is a risk, — for 
instance, that the probability of any given interest 
pa3Tiient is only -^q, in which event it is evident that he 
will not pay $108. We can easily calculate, on the 
basis of the assumed probability, that what has been 
called the "mathematical value" of the bond would be 
$97. This figure is found by multiplying each income 
item by its coefficient of probability and discounting- 
the result at the market rate of interest, 4 per cent. 
We assume here that the risk attached to each indi- 
vidual interest and principal payment is independent of 
that attached to all the others. The probability of receiv- 
ing each payment is -^q, and the risk of its not being received 
is in each case -^q. It is evident that the first payment of $5, 
due in one year, has at that time a mathematical value of 
5 X -^Q, and the present value, when discounted at 4 per cent,, 
would be ^^. If the same expressions be obtained for all 
the other items of income, and the sum total of the present 
valuations be found, it is evident that in the result the factor 
j-^o will appear for every individual sum, and that the total 
will simply be -^-^ as much as though the element of risk were 
absent. In other words, the "mathematical value" of 
the bond will be -^^ of its riskless value of $108, or about 

)7. 

But the actual "commercial value" of the bond will 



Sec. 8] THE RISK ELEMENT 279 

ordinarily be less than this "mathematical value" of $97. 
We may suppose it to be $92.50, indicating a coefficient of 
caution of ^"- Here, as in the case of the lottery ticket, 
we have regarded the actual value of the bond as obtained 
from its riskless value by applying first the probability 
factor, and second the caution factor, ^. 

If the probabilities of receiving the individual interest 
pajnnents were not regarded as independent, the calcula- 
tions of the mathematical value would differ somewhat 
from the preceding. Thus, if we suppose that default in 
one interest payment carried with it, by the terms of the 
contract, the default in all subsequent interest payments, 
we should have to apply the theory of probability some- 
what differently^ but the principle would be the same. 

§8 

There is another way, and one which conforms more to 
ordinary usage, in which the commercial value of the bond 
may be derived from the riskless value. While the price of 
the bond will vary inversely with the risk, the rate of 
interest varies directly with the risk ; so that as the value 
of the bond descends, the corresponding rate of interest 
will ascend. Thus we have riskless, mathematical, and 
commercial rates of interest — 4 per cent, 5.4 per cent, and 
6 per cent — corresponding respectively with the riskless, 
mathematical, and commercial values of the bond — $108, 
$97, $92.50. 

The question sometimes arises, where the element of 
risk thus raises the basis on which the bond is sold, whether 
the 6 per cent is a true "rate of interest." The ques- 
tion is purely one of definition. Were it possible, it would 
be simpler to confine the application of the phrase " rate of 
interest" to an exchange between present and future risk- 
less income. But in this case, it is always exceedingly diffi- 

^ For the consideration of this case, see Appendix to Chap. XVI, § 2. 



280 NATURE OF CAPITAL AND INCOME [Chap. XVI 

cult to state what the riskless rate of interest is, since some 
shght risk attaches to almost every investment. Accord- 
ingly it is usual to regard the commercial rate as a true 
"rate of interest." The best course, therefore, is to recog- 
nize all three as rates of interest, distinguishing them, 
when necessary, as "riskless," "mathematical," and 
"commercial." 

§9 

When we speak of the riskless value or the riskless rate, 
we intend by the employment of the word "riskless,'' 
to exclude from consideration the chance element entirely 
— not only the risk of receiving less, but also the chance of 
receiving more than the specified income. For cases are 
not wanting in which the mathematical and commercial 
values of a security are, by reason of the chance that it 
will prove extra-profitable, more than its riskless value. 
Take, for mstance, a $100 share of preferred stock, on 
which a minimum income of 5 per cent, or $5, is assured. 
If the true rate of interest be 4 per cent, the value of such 
stock should be $125. This is the "riskless" value. The 
mathematical value, however, wUl be greater, say $150, 
inasmuch as there is a probabiUty that the holder will 
receive more than $5 a year, and practically no prob- 
ability that he will receive less. And the commercial value 
wUl be still different, falling, by reason of the caution of 
the investor, somewhat below the mathematical, say to 



Another instance is that of United States government 
bonds. The national banks which invest in these receive, 
besides the interest, a special privilege in the form of per- 
mission to issue bank notes. This additional benefit may 
be regarded as a species of additional income, and materially 
enhances the value of the bonds. For this reason, 
United States government bonds are not used for 
investment purposes, except among those in whom the ele- 



Sec. 10] THE RISK ELEMENT 281 

ment of caution is unduly strong, but are held for the 
most part by national banks. It is therefore misleading 
to cite, as some have done, the rates of interest realized 
on government bonds as an indication of the true rate of 
interest. A similar benefit attaches to the bonds of the 
Credit Foncier in France. These are sold on a very low 
" basis " because of the chance, connected with them, of 
winning prizes. 

§ 10 

In the general case we have to do not simply with the 
risk of falling below a specified income, nor with the 
chance of rising above a specified income, but with both. 
Thus, the dividends from common stock have no fixed 
minimum as do those from good preferred stock, nor any 
fixed maximum as do the interest payments from bonds. 
They may vary, and vary widely, in either direction. The 
amount of variation may be measured with reference to any 
specified amount selected arbitrarily as a basis of com- 
parison. For instance, in the case of stock which has 
yielded, in successive years, the following percentages: 
5, 5, 6, 5, 5, 4, 5, 7, 5,' 3, 4, 5, we may for conven- 
ience take 5 per cent to serve for a basis of computa- 
tion. The stock has yielded 1 per cent or more in excess 
of this in two cases out of twelve ; it has yielded 2 per cent 
in excess in one case out of twelve; it has fallen short by 
1 per cent or more in three cases out of twelve, and fallen 
short by 2 per cent in one case out of twelve. If these fre- 
quencies are our only guide for judging the future, they 
represent the probabilities of receiving the respective divi- 
dends. 

On the basis of the foregoing figures it is possible to calcu- 
late the "riskless" and the ''mathematical" value of the 
stock, and, if we know the caution factor, it is possible to 
calculate the "commercial" value also. Thus, the "risk- 
less" value, in this case, signifies that value which the stock 



282 NATURE OF CAPITAL AND INCOME [Chap. XVI 

would have if it were certain to yield the ( arbitrarily- 
assumed) 5 per cent forever — never more and never less. 
The riskless value is therefore simply the capitalized value 
of a perpetual annuity of $5 per share of $100 face value. 
If the rate of interest is 4 per cent, the result is $5 divided 
by 4 per cent, or $125. 

To obtain the "mathematical" value we simply add to 
the riskless value the value of the chance of getting more, 
and subtract that of the chance of getting less. The 
chance of getting an additional $1 a year is found by expe- 
rience, as set forth above, to be two in twelve, or ^ each 
year. The present value of the right to this chance has 
therefore a mathematical value ^ as great as though the $1 
increment were a certainty. But the certainty of $1 a 
year would be worth $25. Hence a chance of 1 in 6 of 
getting $1 a year would be worth mathematically ^ of $25, 
or $4.16f . In like manner the chance of a second addi- 
tional dollar is one in twelve and is worth (mathematically) 
jL of $25, or $2.08^. These two terms, $4.16f and $2.08^, 
are the additive terms sought. The subtractive terms are 
the mathematical value of the chance of getting $1 less 
than the $5, and of getting still another $1 less. These 
chances, being 3 in 12 and 1 in 12 respectively, are worth 
-^^ of $25 and ^V of $25 respectively, or $6.25 and $2.08^. 
The whole mathematical value is therefore $125+ ($4.16§ + 
$2.081)- ($6.25 + $2,081), or $122.91f. Applying to this 
the factor of caution, which, let us say, is ^^o, we find the 
commercial value to be $110.63. The three values are 
thus, approximately: — 

" riskless " value S125 

" mathematical " value $123 

" commercial " value $111 

In this manner we may compute the three values in any 
other case. Usually, however, the chances involved are so 
indefinite that the reckoning is made only by rule of thumb. 



I 



Sec. 11] THE RISK ELEMENT 283 

Any further attempt to apply the theory of probabiUty 
would therefore outrun the exigencies of practice/ 

§11 

The practical investor, in order to estimate the influence 
of probability, attempts to forecast as nearly as possible all 
the elements which may affect his interests. An example 
occurs in the Engineering and Mining Journal for Decem- 
ber 8, 1904. It is there stated that the mine at Cananea, 
belonging to the Green Consolidated Copper Company, was 
worth, according to quotations at that time, $30,000,000. 
This valuation the journal shows might be justified if we 
suppose the mine to contain a total of 1,040,000,000 pounds 
of copper which can be mined at the rate of 104,000,000 
a year for 10 years, and if we suppose that the price of cop- 
per will be 14 cents, and the cost of production 8 cents, to 
which should be added the expense of refining, selling, com- 
mission, etc., making 2^ cents more, or 10| cents in all. If 
we make allowance for future economies, this may be called 
10 cents, leaving a net profit of 4 cents a pound. On this 
basis we should obtain a 10-year annuity of $4,160,000 per 
annum, the present value of which, at 5 per cent, would be 
$32,000,000. But inasmuch as these forecasts involve 
great uncertainty, a fair price would be regarded as $30,- 
000,000, the discrepancy between $30,000,000 and $32,000,- 
000 being due to the element of risk, i.e. the combined in- 
fluence of probability and caution. This price represents 
a basis of 6|- per cent.^ 

^ Nevertheless it is more than conceivable that the time may come 
when pi'actical brokers will make use of probability computations in 
the same way that they now make use of bond tables. The writer's 
colleague, Professor Norton, has shown this possibility. For a brief 
statement, see Appendix to Chap. XVI, § 3. 

^ For such properties as mines which rapidly depreciate, brokers 
often reckon the "basis" in a somewhat different manner, computing 
the percentage realized to the investor on the supposition that he 
employs a depreciation fund and reinvests, not at the 6i per cent just 



284 NATURE OF CAPITAL AND INCOME [Chap. XVI 

In forecasting the income from capital, it is thus neces- 
sary to forecast all the elements which may influence 
it and also their variability. These elements are some- 
times exceedingly numerous. A stockholder in a railroad, 
in order to obtain a true idea of the value of his property, 
must look forward to the traffic of the road, the price which 
can be charged for this traffic, the cost of operation, in- 
volving the amount of labor, fuel, and materials, the prices 
paid for these items, etc. To forecast any one of these in- 
volves, in turn, some knowledge of outside conditions, as 
the outlook for crops, prices of agricultural products, prob- 
abilities of increased trade through connecting lines, increased 
density of population, possible competition, possible ad- 
verse legislation, etc. 

§12 

We now see that the value of capital actually changes 
through any one of four causes: (1) Through the effect 
of discount ; that is, while no income is being received, the 
value of the capital will rise along a discount curve. (2) 
Through the periodic detachment of income; that is, at 
times when income or outgo occurs, the capital will be 
directly decreased by the amount of the income and in- 
creased by the amount of the outgo reached and passed. 
(3) Through unexpected changes in the rate of interest; 
that is, when such changes occur causing revaluations of the 
future by discounting it at a new rate, the value of the 
capital will change correspondingly — increasing if the rate 
of interest falls, and decreasing if it rises. (4) Through 
unforeseen changes in expected income. 

The fourth cause is the one of most practical importance. 

mentioned, but at the true or safe rate of interest, 5 per cent. On 
this calculation the investor would be found to make 10 per cent per 
annum in addition to the amount set aside for depreciation at 5 per 
cent, and the "basis" would be called 10 per cent. For the case just 
mentioned, this 10 per cent realized, with the depreciation fund re- 
invested at 5 per cent, is equivalent to 6^ per cent realized, with a 
reinvestment at 6A per cent. 



Sec. 12] 



THE RISK ELEMENT 



285 



The market quotations for any product are constantly- 
being changed and revised, not so much through the opera- 
tion of the first three principles as through the fourth — 
the constantly changing outlook into the future. Every 
rumor as to crops, every storm or pest which is known to 
have destroyed them, changes the expectation of future in- 
come. Since the third and fourth causes are both due to 
lack of foresight, they may be included, if desired, under 
the common head of ''risk." 

In Figure 11 the operation of these four causes is repre- 
sented as occurring successively in the order enumerated. 
The capital-value first rises along the discount curve AB, 




constructed according to a particular rate of interest. 
When the first income coupon, so to speak, BC, is detached, 
the value falls to C, after which it travels again along the 
discount curve CD, rising suddenly when a certain 
expected cost DE has been gotten rid of, then following EF 
again, whereupon, in consequence of a sudden and unexpected 
rise in the rate of interest, it falls to G, after which it ascends 
according to the steeper discount curve GH, and then, in 
consequence of a change in the estimate of future income, 
falls again to /, after which it proceeds along another dis- 
count curve to /, and so on indefinitely. The changes 
caused by actual income and outgo, we here represent by 
the continuous lines BC, DE, etc., and the changes due to 
a revised estimate of interest and of income we represent by 
the dotted lines FG, HI, etc. 



286 NATURE OF CAPITAL AND INCOME [Chap, XVI 

§13 

The discount curves just employed are assumed to be the 
same as those employed formerly in the discussion of certain 
prospective income. But, as a matter of fact, chance will 
have an effect even on discount curves. For the increase of 
capital- value along a discount curve is due to the approach 
of expected income, and this approach, in the case of uncer- 
tain income, is quite different from what it is in the case of 
certain income. It is only as the owner has a conviction 
that he is nearing the time when income will be received, 
that the capital- value will increase at all. This will be true 
of dividends for the declaration of which there are defi- 
nitely appointed times; but if the times for the install- 
ments of income are wholly fortuitous, the capital-value 
will not increase and instead of a discount curve, we 
shall have a horizontal line. If a piano dealer is asked 
to value a particular piano in his stock, he will not add 
interest because it had been in his stock a long time. 
It is impossible for him to say which individual piano will 
be sold next, and the mere fact that a particular piano has 
stood for a long time in his store will offer no assurance that 
it will be sold earlier than the others. Therefore the value of 
the piano will not advance with time, but will remain nearly 
at the wholesale price. In the same way, a stock of money 
which a man carries as cash does not advance in value by 
lying in his pocket. For although the services which it will 
render to its owner are actually approaching, their exact 
time of occurrence is not known, but is subject to chance. 
It is chiefly in the case of bonds and stocks, where there 
are definite times for the occurrence of income, that the 
actual value ascends strictly along the discount curve. 
In the case of shares of stock if the stockholder fears that 
a dividend will be small, the value of the stock will only 
slowly increase as the time for the dividend approaches. 
It will follow a discount curve, but one which climbs toward 



Sec. 13] 



THE RISK ELEMENT 



287 



only a slight elevation — enough to represent the commercial 
value of the uncertain dividend. Then when the amount 
of the dividend is known, just before it is distributed, the 
stock (including the right to the impending dividend) 
will suddenly jump in value. After the dividend is paid, 
it will again descend and then increase slowly in value until 
the approach of the next dividend. This will explain the 
fact which has sometimes been observed, that the value 
of a dividend-paying stock often remains fairly constant. 
Normally its course will be somewhat as in Figure 12. 
The capital- value increases only slowly from A to B, when, 
with the declaration of a dividend, it immediately jumps 
to C, and with the distribution of the dividend at D 




Fig. 12. 

descends to E, and so on indefinitely. If we omit the 
fluctuations between the declarations of dividends and the 
distributions, the course of the stock remains relatively 
horizontal, as represented by AB, EF, IJ. 

§14 

The introduction of the element of chance does not greatly 
affect bookkeeping except to impair somewhat the corre- 
spondence between capital accounts and income accounts. 
This is occasioned by mere changes in the size of the 
capital items. When revision of capital- value is due to a 
new estimate of future income, as after a fire, shipwreck, 
or other calamity, the immediate result is merely to reduce 
(or, it may be, to increase) the value of the assets. The 
accountant must "write down" (or up) the assets, and 



288 NATURE OF CAPITAL AND INCOME [Chap. XVI 

therefore also reduce the balancing item on the other side, 
called undivided profits, or profit and loss. But the income 
account is not affected except as the new outlook toward 
the future may lead to new expenses for reconstruction, 
or to new income. 

§15 

Business men try not only to estimate the risks which 
they must encounter and to adjust their accounts accord- 
ingly, but they also endeavor to avoid such risks altogether. 
This follows from the existence of the factor of caution. 
Where the coefficient of caution is abnormal, amounting to 
tncaution, risks are not avoided, but are expressly sought, 
and the phenomena of gambling and indiscriminate specu- 
lation are the result. But in the great majority of men there 
exists a healthy fear of risks, and in consequence a tendency 
to avoid or reduce them. 

There are five principal ways in which risks may be re- 
duced, viz. : — 

1. By increasing guaranties for the performance of con- 
tracts ; 

2. By increasing safeguards against incurring losses ; 

3. By increasing foresight and thereby diminishing the 
risks ; 

4. By insurance, that is, by consolidating risks ; 

. 5. By throwing risks into the hands of a special class 
of speculators. 

These will be considered in order. 

§16 

The ownership of capital wealth necessarily involves 
risk, since the income from it can only be estimated, — never 
precisely foreknown. But it is possible, by a division of 
the ownership of capital wealth, for one class of property 
holders to assume the burden of risks and to guarantee to 
another class a fixed income. This is the primary reason 



Sec. 16] ' THE RISK ELEMENT 289 

for the separation of securities into two great classes called 
stocks and bonds. In any large enterprise the stockholders 
take the risks, and by so doing guarantee to the bond- 
holders a fixed income. As was remarked in a previous 
chapter, the capital stock acts as a buffer between the liabili- 
ties and the assets, which amounts to saying that it guaran- 
tees a fixed income to the holders of the liabilities. Presi- 
dent Hadley has emphasized the fact that a bondholder 
"commutes" the precarious income of an enterprise into 
a fixed annuity and that the system by which one class re- 
ceives "interest" and another "profits" has its origin in the 
desire of one class to avoid and the willingness of another 
to assume risks. ^ 

Nevertheless the general relation between creditor and 
debtor necessarily carries with it a certain amount of risk to 
the creditor. This risk may be reduced by the deposit of 
collateral security or endorsement ^ as in the case of bank 
loans and discounts; by mortgage on real estate, or occa- 
sionally on chattels; by legal regulations, as in the case 
of notes of national banks, and by other methods. 

§17 

The method of guaranties' is really a method of shifting 
risks rather than of avoiding them. The second method 
aims to reduce risk by special safeguards. Some articles 

^ But the "rate of commutation" is not a rate of interest, since 
any ratio of commutation is necessarily a ratio between two incomes, 
those respectively of the stockholders and the bondholders, whereas 
the rate of interest is a ratio of income to capital. 

' The influence of endorsement in reducing risk is greater than 
would appear on the surface. Thus, if there is one chance in a hun- 
dred that the signer of a note will default, and a like chance for his 
endorser, both these risks being independent, the chance that the bank 
will lose is the product of these two, or only one chance in ten thou- 
sand. Hence, two-name commercial paper is ordinarily a safe se- 
curity, provided, of course, the names are those of reliable business 
men, such as have a high "rating" in Bradstreet's or other standard 
commercial agency. 



290 NATURE OF CAPITAL AND INCOME [Chap. XVI 

of wealth exist, in fact, simply for the sake of meet- 
ing sudden unforeseen emergencies. This is true, for 
instance, of fire engines, fire extinguishers, safety appliances 
on railways, safety valves, and other devices connected 
with steam engines and machinery, burglar alarms, safety 
deposit vaults, etc. To a large extent this risk-meeting 
function appUes to almost every stock of wealth. Food 
in a pantry usually exists beyond certain wants in 
order to provide for uncertain wants, and when sources 
of supply are distant, such stores of food need to be large. 
Especially is this true in the case of armies. Again, a 
factory will usually have a large reserve stock, both of 
raw materials and finished products, in order to meet un- 
expected demands. In like manner, jobbers, wholesalers, 
and retailers maintain a sufficient stock of goods to meet 
not only the foreseen, but some of the unforeseen demands 
of their customers. The function of speculators in grain or 
other commodities consists largely in conserving the stock 
of a community as a safeguard against future scarcity. 
Almost all of what is called the reserve of a bank is used as a 
safety fund to meet the unforeseen demands of note-holders 
and depositors, and, in particular, to meet a special "run." 
These reserves often remain as idle as a fire extinguisher for 
years or even decades against the hour of need. It is said 
that there are bars of precious metals in the Bank of England 
which have lain there undisturbed for two centuries. A 
large part of the cash carried by an ordinary individual is 
quite analogous to a bank reserve, being held to meet special 
emergencies. Some individuals even keep in a separate 
pocket a special gold piece, lest some day they should become 
"stranded." It may be said that this risk-meeting function 
of pocket cash is the chief compensation for the so-called 
"loss of interest" on the money thus carried. The con- 
venience and security obtained by having an adequate 
supply is a species of income replacing the income which 
might be earned were the sum invested. The same prin- 



Sec. 18] THE RISK ELEMENT 291 

ciples, from the standpoint of an individual, apply to bank 
deposits, and thus to the whole volume of the circulating 
medium. 

§18 

The third method of reducing risks is by increasing 
knowledge. It has been seen that risk is nothing but an 
expression of ignorance, and decreases with the progress 
of science. It may be said that the chief progress now 
being made industrially consists in lifting the veil which 
hides the future. The countless trade journals now in 
use have their special reason for existence in enabling 
their readers better to forecast the future, by supplying 
them with data as to past and present conditions, as well 
as by instructing them in the relations of cause and effect. 
The government reports of crops, the technical schools 
and agricultural colleges, all tend in the same direction. 
Whereas formerly the mine prospector could only guess 
wildly at the ore "in sight" and the time and cost 
required to mine it, the graduate of mining schools is 
now able, through knowledge of geology and metallurgy, to 
bring these forecasts into some degree of scientific accuracy. 
And, whereas until recently farming was one of the most 
imcertain of occupations, it is to-day — thanks to modern 
scientific agriculture — almost if not quite as amenable 
to prediction as industry or commerce. 

§19 

We come now to that important means of avoiding 
and shifting risks, called insurance. Insurance involves 
the offsetting of one risk by another; that is, the consoli- 
dation of a large number of chances whereby relative cer- 
tainty is, as it were, manufactured out of uncertainty. 
To illustrate this, let us suppose that 10,000 houses of 
the same kind are too distant from each other to be de- 
stroyed by the same fire, and let us suppose that these 



292 NATURE OF CAPITAL AND INCOME [Chap. XVI 

houses in the average would be worth $10,000 each were it 
not for the risk of fire; in other words, that $10,000 is the 
capitalized value of the services to be rendered by each 
house, assuming that it lives out its natural life. The 
value of the total number of houses would then be 
$100,000,000. This is the " riskless value." It is the 
capitalized value of the income which the 10,000 houses 
would bring in, were there no loss by fire. If interest is 
at 5 per cent, the income which is thus capitalized is 
$5,000,000 a year. If now we suppose that the annual 
risk of fire is one chance in 200, there will be about 50 
houses annually burned. Reckoning the value thus de- 
stroyed at an average of $10,000 for each house, there 
will be $500,000 annually lost by fire. We must now de- 
duct this from the $5,000,000, which would be the 
income were it not for fires. We have left $4,500,000, 
the capitalization of which is only $90,000,000. In 
other words, the total property of 10,000 houses is 
worth in "mathematical value" $90,000,000 instead of 
$100,000,000, the reduction being because of the prospect 
of fires. If we suppose all of these houses to be owned by 
one corporation, this mathematical value of $90,000,000 
might also be the actual value, for such a corporation 
could count on about 50 houses burning annually almost 
as a certainty. Each house would then be worth, on an 
average, $9000. But if such an individual house is owned 
by an individual person, this mathematical value would 
not be its " commercial value," on account of the element 
of caution. Let us say that the caution coefficient is |, in 
which case the house would be worth $7000. In other 
words, we have $10,000 as the "riskless" value of the 
house, $9000 as its "mathematical" value, and $7000 as 
its actual "commercial" value, assuming that there is not 
as yet insurance. Now if the owner of such a house could 
secure insurance on a purely mathematical basis of the 
risk, which, as we have seen, is one half of one per cent, 



Sec. 19] THE RISK ELEMENT 293 

and, therefore, could pay only S50 per annum, in consid- 
eration of which the value of his house, if destroyed by 
fire, is restored to him, it is evident that he has made a 
good investment ; for he is now assured of a house even 
should a fire occur, and he has, instead of the risk of fire, 
merely to pay his annual premium of $50 a year, the capi- 
talized value of which is $1000. Consequently, his house 
is worth $10,000 - $1,000, or $9000.^ 

Such an insurance rate, however, being based on the 
mathematical or "pure" premiums, would not pay any 
profit to the companies conducting it. But even a higher 
insurance would leave a large margin of capital- value saved 
to the insured. If we suppose a "loading," so that the in- 
surance premium is not $50 but $100, similar reasoning 
would show that the value of the house when insured would 
be to the owner $8000 instead of $7000. As long as the 
loading is not sufficient to absorb all the margin between 
the $7000 and $9000, it will be advantageous to insure. 

Between the case of a man owning an individual house, 
when the element of caution would have a large influence, 
and that where 10,000 houses are owned by the same corpo- 
ration, in which case the caution element is almost entirely 
absent, there are numberless intervening cases. The larger 
the number of houses owned by one individual or corporation, 
the less profitable becomes insurance. To express it in the 
language of the business man, the various risks insure each 
other. Thus, the North German Lloyd Company finds it 
profitable not to insure its vessels against shipwreck, be- 
cause they have so large a fleet that their losses through 
•a period of time can be counted on fairly well in advance. 

One effect of insurance on the individual is to steady 
the income from his property. The owner of the house in 
question would receive, if it were not insured, a net annual 
income, after providing for depreciation, of 5 per cent on 
$10,000, or $500 a year until the house was burned, after 

^ For a mathematical statement, see Appendix to Chap. XVI, § 3. 



294 NATURE OF CAPITAL AND INCOME [Chap. XVI 

which he would receive nothing ; whereas, if he insures, he 
receives this $500 income less his premium up to the date 
of the fire, and afterward the income from the indemnity 
paid him by the company. 

§20 

The same principles apply to other forms of insurance, 
as marine insurance, which, by consolidating in an in- 
surance company the risk on a large number of vessels, 
reduces for the individual even the perils of the sea to 
relative certainty and regularity; or as steam boiler in- 
surance, which in a similar manner treats the risks of 
explosion; or as plate-glass insurance, burglar insurance, 
Uve stock insurance, hail and cyclone insurance, fideUty 
insurance, accident insurance, employer's liabiUty insur- 
ance, and, above all, Ufe insurance/ This form of insur- 
ance, like the other forms, tends to steady the income of 
the beneficiary. If a wife holds insurance on her hus- 
band's Ufe, the consequence is that, although what he 
gives her during his life is somewhat diminished, her in- 
come will not suddenly cease at his death. The ten- 
dency of insurance here as elsewhere is to make regularity 
out of irregularity, relative certainty out of relative un- 
certainty; and where, under the form of insurance con- 
tracts, the opposite result follows, the case is not one of 
true insurance, but tends to become one of gambhng. 
Thus, if a person insures the life of some one in whom he 
has no financial interest, he is merely gambling on that per- 
son's Hfe. Some years ago in Michigan there was an abuse 
of this type called "graveyard insurance." Speculators 
went through the form of insuring the lives of certain 
old persons, in other words of betting on their deaths, 
a procedure not only vicious as gambling, but calculated 
also to lead to crime. The same considerations apply to 
fire insurance, where a person insures a building in which 
^ See Appendix to Chap. XVI, § 4. 



Sec. 21] THE RISK ELEMENT 295 

he is not financially interested, or over-insures one in which 
he is/ 

The range to which insurance can apply is alv/ays lim- 
ited ; but it is constantly being extended, as business men 
learn how to bring risks of any kind on to a statistical 
basis and to apply the theory of probabihty. At present 
the total assets of Ufe insurance companies alone in the 
United States are nearly $3,000,000,000. 

§21 

Where risks cannot be reduced to a statistical basis, 
and therefore cannot be insured against, recourse is often 
had to the shifting of the risk into the hands of those 
who are willing to take it. Such persons are speculators. 
A speculator is usually one in whom the caution factor is 
not so pronounced as in the ordinary individual. In ex- 
treme cases he tends to become a simple gambler. The 
distinction between a speculator and a gambler, however, 
is usually fairly well marked. A gambler seeks and makes 
risks which it is not necessary to assume, whereas the specu- 
lator is one who merely volunteers to assume those risks 
of business which must inevitably fall somewhere, A specu- 
lator is also usually fitted for his work by special knowledge, 
so that the risk to Mm, owing to superior foresight, is at the 
outset less than it would be to others. The indiscrimi- 
nate prejudice against all speculation, which is so often met 
with, is beside the point ; for, were there no speculators, the 
same risks would have to be borne by those less fitted to 
bear them. The chief evils of speculation flow from the 
participation of the general public, who lack the special 
knowledge, and enter the market in a purely gambling 
spirit. In addition to suffering the usual evil consequences 
of gambling, they produce evil consequences for the non- 
participating public by causing factitious fluctuations 

* For the moral effects of insurance, see Insurance and Crime, by 
A. C. Campbell, Putnam's, 1902. 



296 NATURE OF CAPITAL AND INCOME [Chap. XVI 

in the values of the products or property in which they 
speculate. 

The evils of speculation are particularly acute when^ 
as generally happens with the investing public, the forecasts 
are not made independently. Were it true that each 
individual speculator made up his mind independently 
of every other as to the future course of events, the errors 
of some would probably be offset by those of others. But, 
as a matter of fact, the mistakes of the common herd are 
usually in the same direction. Like sheep, they all follow 
a single leader. How easily they are led is shown by 
the effect on the stock market in the year 1904, when 
Thomas Lawson published scare-head advertisements in 
the newspapers advising the public to sell certain securi- 
ties. 

A chief cause of crises, panics, runs on banks, etc., is 
that risks are not independently reckoned, but are a mere 
matter of imitation. A crisis is a time of general and 
forced liquidation.^ In other words, it differs from any 
other period in two particulars, viz. that the liquidations 
are more numerous, and that they are for the most part 
forced upon the debtors by the creditors because of threat- 
ened or actual bankruptcy. Neither of these conditions 
could exist unless there had been at a prior time a general 
miscalculation of the future. Both creditors and debtors 
must have made a wrong forecast when their ill-fated agree- 
ments were entered into. Hence a crisis is the penalty 
which must be paid when a previous general error in pre- 
diction is discovered. Such a general error may be due to 
the coincidence of a number of independent mistakes of 
individuals ; but it almost always is due to lack of inde- 
pendence, — to the principle of imitation. The error, 
whatever it is, when committed by a person of influence, is 
Uke an infection; it is caught by hundreds of others and 

' See Juglar, Des Crises Commerdales, Paris, 2d edition, 1889, 
Chapter I. 



Sec. 21] THE RISK ELEMENT 297 

transmitted to thousands. A great mob of easily led in- 
vestors, eagerly searching for "straight tips" which may 
bring instant wealth, make their mistake in common, and 
when the mistake is disastrous they try, en masse, to escape. 
A sudden rush of all the passengers on a ferry-boat to one 
side will produce a " list " in the boat's position, and some- 
times cause it to capsize, though the independent move- 
ment of the individual passengers will seldom or never 
produce disaster. So also the sudden general realiza- 
tion of unforeseen danger on the part of the investing 
public may submerge the craft of credit and those whom 
it has hitherto borne along in safety. In short, a general 
crisis bears the relation to individual bankruptcies which 
a general conflagration bears to individual fires. The key 
to the study of either crises or conflagrations is the exist- 
ence, in place of independent hazards, of interdependent 
ones. So far as conflagrations are concerned the prin- 
ciple of interdependence is distinctly recognized by stu- 
dents of fire insurance, and in consequence, each company 
strives to keep its own fire risks independent of each 
other, by not having too many in the same locality; but 
so far as crises are concerned, the principle has not yet been 
sufficiently emphasized by students of economic history. 

The same principle applies to the phenomenon of a run 
on a bank. The opinions of the bank's solvency are not 
formed independently but interdependently. A year or 
more ago the newspapers reported that, a policeman and 
a crowd of people being collected on the steps of one of 
the Wilkes-Barre savings banks to escape the rain, two 
Hungarian depositors who were passing jumped to the 
conclusion that the bank had been attacked by burglars, 
and circulated the disturbing news in the Hungarian 
colony, with the result that when the bank opened for busi- 
ness many depositors made a run upon it. 

We see, then, that where speculation is imitative, it is 
dangerous alike to those who engage in it and to the public. 



298 NATURE OF CAPITAL AND INCOME [Chap. XVI 

Where, on the other hand, speculation is based on independ- 
ent knowledge, its utility is usually enormous. It oper- 
ates both to reduce risk by means of utilizing the special 
knowledge of speculators, and also to shift risk from 
those who lack this knowledge to those who possess it. 
The consequence is that normally speculative property will 
gravitate into the hands of those most able to forecast its 
true income. 

Modern production has been called capitahstic-specula- 
tive production, owing to the fact that it is managed by 
"captains of industry," who are specially fitted at once to 
forecast and to mould the future within the special realms 
in which they operate. The industries of transportation 
and manufacturing particularly are under the lead of an 
educated and trained speculative class, whose function it is 
to assume for themselves the main risks, and leave the 
ordinary investor, who is not so equipped, to cooperate as 
a mere "lender" or silent partner. Yet it often happens 
that they betray the confidence placed in them, and con- 
tinue to throw the burden of risk on those whom they 
pretend to shield. 

§22 

In the special field more usually known as "speculative," 
— namely, that in which attempts are made to forecast 
prices in the great exchange markets, — we find a similar 
class who are specially trained. These speculators are 
either "bulls" or "bears"; that is, they speculate either 
for a rise or a fall. Those who believe that wheat 
or any other article is likely to rise in value and hence 
yield more than the "rate of interest," will hold it. Or if 
they do not own it, will buy it or obtain an option on it. 
Such an option is known as a "call," and is put in force at 
a later time, at a price fixed in advance and considered 
low. On the other hand, those who believe that prices 
will fall will sell out their present holdings, or may seU 
"short," agreeing to supply such holdings at a later time 



Sec. 22] THE KISK ELEMENT 299 

at a fixed price which they consider high. Such a contract 
to sell is often made in the form of an option, in which 
case it is known as a "put." 

To show how such contracts will shift risks, a few exam- 
ples will suffice. A building contractor who had taken a 
large contract was asked if he were not taking large risks, 
since he could not foreknow the cost of building. He re- 
plied, "No, I am taking no risks at all except on 'labor'; 
I have made contracts to be supphed with all materials 
when needed, at fixed prices." Those who made these con- 
tracts thus assumed the risk of fluctuation in price in the 
special materials in which they dealt, relieving the con- 
tractor of the necessity of informing himself of the special 
market conditions for stone, brick, timber, etc., and ena- 
bling him to make a closer bid for the contract, inasmuch 
as there was less need of the element of caution. The pub- 
lic, of course, get the benefit of such a shifting of risk 
in the form of reduced cost of building. Similar results 
follow from most other "short" sales. Again, a woolen 
manufacturer need not carry so large a stock of wool if he 
can make a contract by which some one will sell short, or 
agree to supply the wool at fixed prices and at certain 
dates. He can afford to use up his present stock fear- 
lessly, with the certainty that when it is gone he can 
obtain a new supply.^ Without such a contract, he would 
be under the necessity of carrying a large and idle stock. 

An important method of shifting risks is "hedging," 
whereby a dealer, for instance in transporting wheat, may 
be relieved of the risk of a change in price. He buys 
wheat in the West intending to ship it to New York and 
sell it there at enough to cover cost of transportation 
and a small profit. In consequence of a sudden fall in 
price he might find all his profit wiped out ; or he might, 
on the other hand, by a rise in price, make much more 
than normal profits. But, being of a cautious disposition, 

1 Cf. Hadley, Economics, Putnam's, 1896, p. 106. 



300 NATUKE OF CAPITAL AND INCOME [Chap. XVI 

he prefers an intermediate course, — a small profit which 
is sure, rather than the chances of both gain and loss. 
Consequently he "hedges." He enters into some specu- 
lative market, knowing that it will move in sympathy 
with the New York market, and there he "speculates" 
for a fall, or sells "short." In case the price in New York 
falls, what he loses on the wheat which he has transported 
he gains through his speculative short selling. Contrari- 
wise, if the price rises, what he gains on his wheat trans- 
ported he loses in the speculative market. In other words, 
he is, as it were, betting on both sides of the market at 
once, and therefore eliminating all risk, so that he only 
obtains his normal profit, commission, or percentage on 
the actual wheat handled, having imposed the burden of 
risk of speculation on the speculative dealers to whom he 
sold short.^ 

The effect of hedging on those who engage in it, 
such as the wheat dealers, is evidently to enable them to 
work on a smaller margin of profit. In consequence the 
public receives a benefit in lowered prices. The case is 
thus very similar to those respectively of the builder and 
of the woolen manufacturer. Short selling, binding the 
future to the past, enables the specialist to guarantee 
to the general public a definite foreseen series of events. 
The beneficial effect to the public, in saving useless stocks 
and reserves, in producing more intelligent direction of en- 
terprises, and in encouraging accumulation through greater 
certainty of its future benefits, is both obvious and great. 
Risk is one of the direst economic evils, and all of the de- 
vices which aid in overcoming it — whether increased guar- 
anties, safeguards, foresight, insurance, or legitimate specu- 
lation — represent a great boon to humanity. 

^ See " Speculations on Stock and Produce Exchanges of the United 
States," by Henry C. 'Emery, Publications of American Economic Asso- 
ciation. For the development of insurance-speculation in England, 
see " The Put and Call," by L. R. Higgins, London, Effingham WU- 
son, 1902. 



PART IV. SUMMAKIES 

Chapter XVII. Summary of Part III 
Chapter XVIII. General Summary 
Glossary. Summary of Definitions 



CHAPTER XVII 

SUMMARY OF PART III (CHAPTERS XI-XVl) REPRESENTED 
BY DIAGRAMS 

§1 

We have finished our study of the relations between 
capital-value and income-value and may now pause to 
summarize them briefly. At the beginning of Part III it 
was stated that the income from capital wealth consists 
of whatever service it performs for man ; that capital and 
income may each be measured either in specific quantities 
of their respective units, or in value ; and that consequently 
there are four ratios between income and capital; namely, 
(1) the physical productivity of capital, (2) the value pro- 
ductivity, (3) the physical return, and (4) the value- 
return. Our special theme has been the value-return, — 
the relation between income-value and capital-value. 

We saw that the value of capital wealth is the discounted 
value of its expected income. The relation between the 
value of the income and the value of the capital was indi- 
cated by diagrams. Income was represented by a series 
of vertical hues as in Figure 13 (a, a', a", a'"), the hori- 
zontal distances between them representing intervals of 
time. It was then found possible to represent the capital- 
value of this income in anticipation, on the assumption 
that the income could be relied upon with certainty. 
This representation gave the capital curve, — a broken or 
toothed curve AB. In this curve, each vertical drop is 
equal to the corresponding income item shown below it, 
and the intervening points are connected by discount 

303 



304 



NATUKE OF CAPITAL AND INCOME [Chap. XVII 



curves; so that the total capital- value at the time G is 
represented by the altitude BG. 

But this separate representation for capital and for in- 
come respectively need not be adhered to, because the 
capital curve AB alone contains in its vertical teeth all 
that is necessary to indicate the installments of income ; and 
in the present chapter the main propositions relating to 




Fig. 13. 

capital and income will be restated with the aid of geo- 
metrical representations of which this capital curve AB 
is the type. 

§2 
First of all, such a curve exhibits the fact that the value 
of any capital is the discounted value of the expected in- 
come. In Figure 14 the several discount curves used in 
previous diagrams are all continued to meet OB. The 
parts into which GB is thus divided, 6, &', h" , V", will 
represent respectively the present values of the income 
items a, a', a", a'". This may readily be proved from 
the nature of the discount curves. 



Sec. 2] 



SUMMARY OF PART III 



305 



The diagram shows, in the second place (tracing it for- 
ward chronologically), that the capital- value alternately 
rises and falls, rising in anticipation of approaching income 
and falling as the installments of this income are, like cou- 
pons, successively detached from capital. The alternate rise 
and fall of the capital curve may be equal, each to the other, 
indicating that the income is "standard"; or the former 




Fig. 14. 

or the latter may be the greater, indicating respectively 
that the income is above or below standard. 

If any installment of income is negative — in other 
words, is not strictly income, but outgo — we need simply 
to reverse the direction of one of the teeth, as in Figure 
15. In this case the capital- value is simply the discounted 
value of the future income less that of the outgo. 

§3 

As we have seen, if we trace the entire history of a capital 
curve backward in time from the last installment of income 
to the beginning of the investment or enterprise, the curve 



306 



NATURE OF CAPITAL AND INCOME [Chap. XVII 



will normally be at the zero point at both ends. This 
is shown in Figure 16. Such a curve shows the normal 
cycle of capital-value from the moment when the article 
of capital is first utilized to the moment when it is ex- 



FiG. 15. 

hausted. It is "normal" in the sense that the income is 
just sufficient to compensate for the outlay, no more and 
no less, and that usually the principal items of outgo all 
occur in the early part of the cycle, and the principal 
items of income all accrue in the latter part. In such a 




Fig. 16. 



normal curve the capital-value (AB in Fig. 16) at any 
moment may be said to represent two things : first, it rep- 
resents the discounted value of the future expected income 
(less that of future expected outgo, if any) ; and, secondly, 



Sec. 3] 



SUMMARY OF PART III 



307 



it represents the accumulated value of past outgo (less that 
of past income, if any). From this it follows that the 
value of the capital AB is, on the one hand, less than 
the future total income which it represents, and greater 
than the past outgo. This capital- value may be regarded 
as made up of the elements 6, h' , h'" , which are respec- 
tivel}^ the discounted values of the respective larger mag- 
nitudes a, a', a"; and, on the other hand, as made up of 



a' 



A 
Fig. 17. 



b'", 6'^, If, which are the accumulated values of the respec- 
tive smaller magnitudes a'", a'^, a^. By puttuig together 
the elements of which AB is composed, we see, on the one 
hand, that AB is less than the anticipated income and 
greater than the past outgo; and consequently, a fortiori, 
that the past outgo is less than the future income. For 
the sake of simplicity in our illustration, we have chosen a 
point of time after all the outgo and before any of the in- 
come has accrued ; but the same principles could be worked 
out upon such a diagram, no matter what point of time were 
chosen. In other words, in the normal case the value of any 
capital is intermediate between the value of its past cost 
of production or acquisition and the value of its future 
income. 



308 



NATUKE OF CAPITAL AND INCOME [Chap. XVII 



In the special case in which there is but one item of cost 
and one item of income, the curve is reduced to that shown 
in Figure 17, where a is the expected income, and a' the 




Fig. 18. 



past outgo. If the capital-value AB be taken at a point 
midway between the income and outgo, it evidently fol- 



6" 



c" 



Fig. 19. 



lows, by the nature of the discount curve, that the ratio 
of a' to AB is the same as the ratio of AB to a, or that 




Fig. 20. 



AB is the "mean proportional," or "geometric mean," 
between a and a' . In other words, the normal relation 
between cost, capital, and return is expressed in the state- 



Sec. 4] SUMMARY OF PART III 309 

ment that the capital is a mean proportional between its 
past cost and its future return. 

§4 

Another use which may be made of the diagrammatic 
representation is to exhibit in a compact manner the sum- 
mation of both the capital and the income of any given 
enterprise or community. This may be done simply by 



Fig. 21. 

adding together the corresponding ordinates or vertical 
lines in any number of capital curves, representing any 
number of articles of wealth or property. Let Figure 18, 
for instance, represent one capital curve, and Figure 19 an- 
other. Figure 20, formed by combining Figures 18 and 19, 
then represents the sum of the capital and income of both. 
Figure 20 is derived from Figures 18 and 19 in such a 
manner that the ordinate B is the sum of the individual 
ordinates 6' and h", and in like manner any other ordinate, 
G, is the sum of the corresponding individual ordinates c' 
and c". From the rule by which Figure 20 is constructed, 
it is evident that every tooth in the constituent curves, 
such as a' and a", will be reproduced in the combined dia- 
gram. In Figure 20, therefore, the ordinates represent the 
combined capital-values at various points, while the two 
teeth a" and a' represent the total income accruing in that 
time interval which includes them. Thus, Figure 20 epito- 
mizes the summation both of capital and income. 



310 



NATURE OF CAPITAL AND INCOME [Chap, XVII 



But it is not necessary to have three separate diagrams. 
It is possible to superimpose one of the first two figures 
upon the other, as shown in Figure 21. In this figure, on 
the same axis XF is drawn first FG, corresponding to Fig- 
ure 18 above, and, secondly, at distances above FG corre- 
sponding to the ordinates in Figure 19, is drawn the line 
MN . This line MN contains an apparent tooth or break 
which does not appear in Figure 19, but this is only for 
the purpose of preserving at this point the prescribed dis- 
tance from the line FG. Considered relatively to FG there 




Fig. 22. 



is no break. Thus the line MN , measured relatively to 
FG, takes the place of the constituent curve of Figure 19, 
and measured relatively to the base line XF it represents 
the combined curve of Figure 20 for both constituents. 

The same method applies where there are any number of 
constituent capital curves. Thus (Fig. 22), let us draw for 
our first capital curve one which has an income item a, 
and superimpose upon it a second capital curve, of which 
the income item is a' , and so on. The capital curve at 
the top will represent the total of the individual capital 
curves beneath it, and each belt between — namely, the 
difference between any two neighboring capital curves — 
will replace a constituent curve. From the manner of 
their construction it is clear that the income item a' will 
be carried forward successively to each of the curves above 
it, and will be represented by a tooth in the curve at the 



Sec. 5] 



SUMMARY OF PART III 



311 



top, as represented by the clotted lines. Similarly, a' , a", and 
a'" are transmitted to the top. The final curve at the 
top thus shows in its separate teeth all the income items 
contained in the curves of which it is the sum. 

§5 

In case two teeth in separate curves occur at the same 
instant, the combined curve will, of course, have a large 




Logging Camp 



Fig. 23. 

tooth equal to their sum. In case one tooth is positive, 
representing income, and the other is negative, or outgo, 
the coincidence of these will result in a small tooth equal to 
their difference, and this difference will be zero if the two 
items are equal. 

The most important case of this kind occurs when there 
are" interactions." It has been explained that an interaction 
is an income item for one capital which at the same time 
is an outgo item for another. If the curves for these two 
capitals are superimposed, the equal income and outgo items 
will cancel, and the resulting combined curve will be un- 
broken at the point representing the time of interaction. 
This is shown in Figure 23, giving the typical history of 
limiber operations. Every year a logging camp yields a 



312 



NATUKE OF CAPITAL AND INCOME [Chap, XVII 



certain amount of logs, the turning out of which is credited 
to the camp, but debited to the mill. In the diagram, 
the space between the base line and the first curve above 
it represents the capital curve of the logging camp, and 
the space above this curve represents the capital curve of 
the sawmill. At the time of the transfer of logs from 
the one category to the other, there is a corresponding 
diminution in the capital-value of the logging camp, but 
an increase in the capital-value of the sawmill. 

The characteristic of such an interaction or couple is 
that it leaves unbroken the upper curve of final summation. 



SaolinE 



Tree 



C 
Fig. 24. 



There is no carrying forward of teeth, as by the dotted lines 
in the previous diagram, — or rather, the carrying forward 
results in a cancellation. The interaction is merely a 
sacrifice of one capital for the benefit of another, and does 
not disturb the total. 

If the interaction BG is greater than we have represented 
it in the diagram, so that G is lower and B higher than in- 
dicated, the discount curve AB will be nearer coincidence 
with MN, and GD nearer coincidence with XY. We may 
suppose a case in which coincidence is reached. This case 
is represented in Figure 24. Here BG represents such an 
interaction as occurs when one capital good is completely 
transformed into another, as when the " sapling" becomes a 
" tree " at a certain definite point of time. The capital-value 



Sec. 5] 



SUMMARY OF PART III 



313 



of the sapling disappears at BC, but there appears in its 
stead the capital- value of the tree. The change from one 
to the other is evidently entirely nominal, and it is possi- 
ble, by drawing any other vertical line than BC, to create 
an 'interaction" simply by calling the portion on the two 
sides of this line by different names. 

When, as in Figure 25, a series of curves is constructed 
and superimposed to represent the income from any speci- 
fied group of capital instruments, the sum total of the income 
is evidently represented by the entire series of teeth in the 




Fig. 25. 



top curve. These teeth form a physical picture of the 
"outer fringe" of services, which was discussed in 
previous chapters. If in the diagram we omit the upper- 
most layer of capital, the curve remaining immediately 
below this layer will then be the outer fringe for the entire 
series of capital instruments below it. We may pro- 
ceed step by step in either direction, leaving off an item of 
capital or taking one on. In every case the outer fringe 
of teeth wiU represent the sum total of income for the group 
of capital represented below it. 



314 



NATUKE OF CAPITAL AND INCOME [Chap. XVII 



In Figure 25 all the teeth below the top layer are rep- 
resented to be interactions. But if any of them should 
be final services, they need only be carried forward by dotted 
lines to the top, as in Figure 26, Or if the capital repre- 
sented by one layer interacts with the capital represented 
by a layer two or more removes above it, the connection 




Fig. 26. 

will be represented by carrying forward the tooth by dotted 
lines to the proper stage. 

As we are at present interested in the general aspects 
of the subject, we need not take into account such complica- 
tions, but may assume, for purposes of exposition, that all 
capital can be arranged in a single definite series, each mem- 
ber of which acts upon the one above it, and so on to the 
end. In the actual world, it is usually possible to arrange 
capital roughly in such an interacting series. 

§6 

Two special applications may be made of the foregoing 
representation for the summation of capital curves. The 
first will show the total value of capital property and the 
total value of income possessed by a particular individual, 
and the second will show the same condition as to an entire 
society. 



Sec. 6] 



SUMMARY OF PART III 



315 



We may suppose a man's capital to be divided into 
three classes: first, money-paying investments; second, 
money; third, enjoyable articles purchased by money. 
We may juxtapose these elements, as in Figure 27. 



"U-- 



Enjoyable Capital 



Money 



Investments 



Fig. 27. 



Here, whenever an investment pays money, a tooth 
is produced in the first curve and a transaction 
takes place between the categories "investments" and 
"money." By each such transaction the investments are 
reduced in value by the amount of coupons detached, and 
the stock of money is increased by the same amount. In 
like manner, every time money is spent, a transaction takes 
place between the belt representing money and that repre- 
senting enjoyable capital. By such transaction the money 
stock is depleted, and the value of the enjoyable capital 
increased by the same amount. These operations are 



316 NATURE OF CAPITAL AND INCOME [Chap. XVII 

therefore self-canceling and are not transmitted to the 
outer fringe. The total income, therefore, from the entire 
group of capital, is represented simply by the vertical un- 
dulations in the top curve. 

By means of this diagram we may see clearly the various 
meanings of "individual income." The business man 
usually applies the term to the teeth of the investment 
curve ; the economist to the teeth next above in the money 
curve, or the teeth above that in the curve representing 
enjoyable capital. Practically, it does not greatly matter 
which of the three we select, since usually, for any con- 
siderable period of time, all will closely correspond. This 
must needs be so, unless the stock of money or enjoyable 
articles is appreciably increasing or decreasing. These 
exceptional cases have already been discussed in detail, 
and there is no difficulty in representing them by diagrams. 



The other application of our diagrammatic summation is 
to present a fairly complete picture of the total value of 
capital-wealth and the total value of income of an entire 
society. In the capital of a community it is not usual to 
include human beings, and for that reason it is scarcely 
worth our while to discuss the theoretical questions as to 
the manner in which they might be included in such a rep- 
resentation. As a matter of fact, the method of capitaliz- 
ing human beings will vary with the special purpose in 
view. Our present purpose is chiefly concerned with in- 
teractions between man and other capital, and we need 
practically only to capitalize the money-earning power of 
the individual. This part of the capital-value of a man 
we may call "labor power." We then have the total capi- 
tal of a community consisting of labor power, land, inter- 
mediate capital, and enjoyable capital, as in Figure 28. 
For convenience, and to avoid needless complications, we 
assume that labor power interacts only with land, land 



Sec. 7] 



SUMMARY OF PART III 



317 



with intermediate capital, and intermediate capital with 
enjoyable capital. The income from the entire series is 
represented, as before, by the teeth of the uppermost line. 
From this diagram we see that the total income of a com- 
munity comes through enjoyable goods. The other capital 
items produce income, but this income is in every case also 




Intermediate Capital 
Land 



Labor-power 



Fig. 28. 

an outgo with reference to the layer of capital next above. 
Many of the fallacious methods of summing income consist 
virtually in adding together the teeth in the various layers. 
It is forgotten that the teeth below the top layer are interac- 
tions and therefore both positive and negative — positive 
with reference to the layer below and negative with refer- 
ence to that above — and that therefore they come into 
the summation of income only to go out again. Their 
function in each case is simply to keep up the capital in the 
layers above. Without their activities these layers above 
would soon be exhausted, and the income at the top would 
not continue for long. 

§8 
From this point of view, each interaction may be con- 
sidered as the discounted value of a certain portion of the 



318 



NATURE OF CAPITAL AND INCOME [Chap. XVII 



items of income from the layer next above. In Figure 
29 the interaction a may be taken as the discounted value 
of the income taken from the layer next above, between 
the points P and Q. Here we have a geometrical repre- 
sentation of the fact so often insisted upon by Professor 
Bohm-Bawerk^ and Professor Taussig,^ that the pro- 
duction of this year's wool is for next year's (or next 
month's) yarn, of this year's yarn for next year's cloth, of 
this year's cloth for next year's clothes, etc. 

In tracing the connection between the income items in 
different layers, we may consider either a cross-section be- 
tween the different layers, by drawing two vertical lines 




Fig. 29. 



separated by a certain interval and noting the intervening 
income taking place simultaneously in the various layers; 
or we may follow the successive time connections involved 
between one layer and the next. In the treatment which 
has been given in the previous chapters, the former method 
was emploj^ed. The present diagrammatic representation 
gives us a bird's-eye view of both. Thus, in Figure 30, 
representing the logging camp, sawmill, lumber yard, etc., 
having selected a period represented between the vertical 
line drawn at A and B, we may either address ourselves to 
the mutual relations of the various layers there comprised; 
or we may address ourselves to the income item a, whose 

1 Positive Theory of Capital, English translation, 1890, pp. 179-189. 

2 Wages and Capital, New York (Appleton), 1896, Chapters II, III. 



Sec. 8] 



SUMMARY OF PART III 



319 



influence traverses the entire section. It is produced by 
the logging camp; ''ripens" into all that income of the saw- 
mill which is comprised between the points P and Q ; and 
this in turn ripens into the income of the lumber yard 




comprised between the points P' and Q' . In this way we 
are virtually following the log as it is transformed in the 
various processes from tree to lumber. 

It is in consideration of such a relation or set of relations 
that an income item like a was called a "preparatory 
service." Each such preliminary process of production 
takes place in anticipation of future resulting processes, 
and derives its value from them. Combining this principle 
with the principle that the value of all capital is the dis- 
counted value of its expected income, we see that the value 
of the capital in the lower layers is ultimately dependent 
on the value of the income in the topmost layer; for the 
value of that earlier capital is the discounted value of the 
income it produces, and this income, consisting of interac- 
tions or preparatory services, is in turn the discounted value 
of the services to which it leads, and so on through succes- 



320 



NATURE OF CAPITAL AND INCOME [Chap. XVII 



sive layers to the top, as seen in Figure 31. Here AB, 
the capital-value of the lowest layer, is the discounted 
value of the income from that layer, namely the teeth 
a, a', a", but this income in turn is the discounted value 
of the income represented by the teeth intervening be- 
tween P and Q from the layer next above, and this income 
in turn is the discounted value of the income between P' 




Q Q 



Fig. 31. 



and Q' on the layer still above. In this representation 
the curves are shown as all terminating in the base line ; 
but the representation may readily be extended to the case 
of an income infinitely continued. 

§9 

In Chapter XVI it was shown that certain modifications 
needed to be introduced into our theory of the determina- 
tion of capital-value when the element of uncertainty was 
introduced. We are fresh from the discussion of these, and 
they need no extended mention here. The main point to 
be kept in mind is that when the element of chance is 
taken into account, sudden breaks occur in the capital curve, 
so that instead of following the simple order previously 
indicated, beginning at zero and ending at zero, with inter- 
mediate teeth alternately rising and falling along the dis- 
count curve, it suffers additional interruptions at points 
where the estimates of future chances are changed. 

The most important point in the life history of such a 



Sec. 9] SUMMARY OF PART III 321 

curve of capital-value is at the beginning. When the ele- 
ment of chance or luck is taken into account, the capital 
curve is less likely to begin at the zero line. It may begin 
at some point above ; it will not begin at any point below ; 
for if the present value of the chance of gain did not out- 
weigh the present value of the chance of loss, the enterprise 
would never be undertaken at all. In the great majority 
of cases, the capital-value at the outset of an enterprise 
is greater than zero ; that is, in the estimation of those who 
enter into it, the gains will not only pay for the costs with 
interest, but something in addition, even when the element 
of chance is included in the discounting operation. At any 
rate, it is not infrequent that when a new enterprise 
is started, those who have the first knowledge of the 
possibilities, and the first opportunity to exploit them, 
expect returns out of proportion to the ordinary rate of 
interest and compensation for risk. The only reason this 
is not more generally true is because of the existence of 
competition, by which the special advantage of individuals 
through special knowledge, foresight, etc., is offset by the 
vigilance of their rivals. 

With these points in mind, we observe that the history 
of the value of any particular article of capital-wealth may 
be represented as in Figure 32. Starting at A, some point 
above the zero fine, the capital-value rises to B, because, 
let us say, of the first expenditure involved. From B it 
proceeds along a discount curve to C. There, through the 
influence of the risk element, it suddenly drops to D, at 
which point some new information has reduced the prospect 
of future gain or increased the risk of future loss. From D in 
turn it proceeds along the discount curve to E. At this point 
the cost EF is incurred, but at the same time confidence as 
to the future receives a shock, and instead of proceeding 
from F, the curve drops at once to G. Thence it rises gradu- 
ally and normally to H, when the first income item, HI, 
is received. This being, let us say, less than was anticipated, 



322 



NATURE OF CAPITAL AND INCOME [Chap. XVII 



it shows that the capital-values had been hitherto too high. 
Consequently the curve drops to J, and thence proceeds 
in the manner indicated in the diagram, ending at the zero 
point P, when the last installment of income OP is received. 





Fig. 32. 

In this chapter we have treated income as accruing dis- 
continuously ; but it is not difficult, in accordance with the 
suggestions made in a previous chapter, to extend the prin- 
ciples to apply to the continuous case. It would also 
be possible, were it worth while, to exhibit, by means 
of similar diagrammatic representations, numerous proposi- 
tions other than those already noted. Our object, however, 
has not been to exploit the diagrams, but merely to use them 
for a running epitome of the general relations existing be- 
tween capital and income. 



CHAPTER XVIII 

GENERAL SUMMARY 
§1 

It has been the endeavor m the preceding chapters to 
give a definite picture of the mass of capital and its services 
to man. In such a picture we see man standing in the 
midst of a physical universe, the events of which affect 
his life. Over many of these events he can exercise no 
control or selection ; these constitute his natural environ- 
ment. Over others he exercises selection and control by 
assuming dominion over part of the physical universe, 
and fashioning it in new shapes to suit his needs. The 
parts of the material world which he thus appropriates 
constitute wealth, whether they remain in their natural 
state or are "worked up" by him into products to render 
them more adapted to his needs. This mass of instru- 
ments will consist, first, of the appropriated parts of the 
surface of the earth, of the buildings and structm-es 
attached to the soil, and of the movable objects or "com- 
modities" which man possesses and stores in the buildings 
upon the earth; and, secondly, of the persons of the 
human population itself, — for these, though they are also 
the abode of the owner of wealth, are themselves objects 
owned. 

This mass of instruments serves man's purpose in so far 
as its possession enables him to modify the stream of his- 
torical events. By means of land and the modifications 
which he makes upon it he is enabled to increase and im- 
prove the growth of the vegetable and animal kingdoms 

323 



324 NATURE OF CAPITAL AND INCOME [Chap. XVIII 

in such a way as to supply him with food and the mate- 
rials for constructing other instruments. By means of 
dwellings and other buildings he is enabled to divert the 
elements from contact with his body and with the objects 
of wealth which he stores in them. By means of machin- 
ery, tools, and other instruments of production, he is 
enabled to fashion new instruments to add to his stocks 
or to take the place of those destroyed or worn out. By 
means of the final finished products which minister to his 
more immediate enjoyments, such, for instance, as food, 
clothing, books, ornaments, he is enabled to consummate 
the objects for which the entire mass of wealth is produced 
and kept in existence, namely, the satisfaction of his de- 
sires, whether these be for the necessities, the luxuries, the 
comforts, or the amusements of life. In these and other 
ways the stock of wealth will modify the course of natural 
events in ways more or less agreeable to the owner. These 
changes in the historical stream of events which occur by 
means of wealth constitute what have been called the serv- 
ices of wealth. 

In our picture, therefore, we observe (1) a stock of instru- 
ments existing at an instant of time, and (2) a stream of 
services through time, flowing from this stock of wealth. 
The stock of wealth is called capital, and its stream of serv- 
ices is called income. The income is the more important 
concept of the two, for the capital exists merely for the 
sake of the income, and the ownership of the capital has no 
other significance than the ownership of possible income 
from that capital. The division of income between differ- 
ent owners constitutes in reahty a division of ownership 
of the capital which bears the income, and the individual 
shares constitute what are called property rights. 



From this it is apparent that property rights and wealth 
go side by side, and that neither can exist without the other, 



Sec. 2] GENERAL SUMMARY 325 

property signifying merely the sharing of wealth among 
individuals. When we piece together these shares, we ob- 
tain the ownership of all wealth. In like manner, the value 
of the entire mass of wealth must be taken to mean simply 
the sum of the values of the individual shares of this owner- 
ship. When we attempt to reach this total by combining 
the shares of individuals, we do so by making a careful 
record of all "capital accounts." In such a record we find 
that many items occur in pairs, — negative items of 
property or "liabihties" in one account and positive items 
or "assets" in another. By this pairing of items, there 
will be left as the final sum of property value the 
value of the entire stock of physical instruments. 

Of the services which flow from the stock of capital, 
it has been seen that the great majority consist merely 
of "interactions" between one category of capital and 
another. All that is accomplished by most instruments 
of capital is to hand over something to other instruments of 
capital. The great mass of capital — lands, warehouses, rail- 
roads, machinery, ships, etc. — exists either for "transpor- 
tation," that is, for changing the position of wealth from 
one place to another; or for "production," that is, for chang- 
ing wealth from one state or form to another; or finally 
for exchange, the mutual transfer of rights to wealth. In 
every such operation, the instruments which have wrought 
the change are said to have rendered a service ; and in the 
income account these instruments are credited with the 
value of such services ; while the instruments which receive 
the services, and are thus improved in position or condi- 
tion, are said to have rendered a disservice and are at 
the same time debited with exactly the same item. When 
we thus come to put together the entire total of income, 
all such pairs of items or "interactions" cancel. These 
double-faced events or interactions constitute the over- 
whelming mass of items in the actual inventory of income 
which enter into the accounts of business men. Out of 



326 NATURE OF CAPITAL AND INCOME [Chap. XVIII 

this fact, combined with the fact that every " transaction " 
is also double-faced, grows, as we have seen, the entire 
theory of double-entry bookkeeping. 

Out of the entire mass of instruments thus acting and 
reacting upon each other, there finally emerges an uncan- 
celed or net income which does not represent a mere transfer 
from one category to another within the mass, but an actual 
contribution issuing from the mass to the benefit of man, 
the owner. These final elements are his real income. In 
the last analysis they consist purely of subjective or psychic 
satisfactions; that is, of conscious desirable experiences. 

§3 , 

But these desirable mental experiences occur at the sacri- 
fice of certain undesirable ones, namely, of efforts. The 
subjective efforts put forth for the sake of subjective satis- 
factions constitute the net or uncanceled elements of outgo. 
Thus we see that, side by side with the objective income 
and outgo stream, and as the final result of that stream, there 
exists its subjective counterpart, namely, the stream of ef- 
forts and satisfactions. In the same way, there exists, side by 
side with the objective mass of capital, the subjective esteem 
in which this capital is held, namely, what we have called 
its desirability, or utility. If efforts and satisfactions are 
called subjective income, desirabiUty or utihty should be 
called subjective capital. The same antithesis of time 
appHes to the subjective as to the objective; desirabihty 
is a state of mind at an instant of time ; efforts and satis- 
factions are experiences through a period of time. Desir- 
ability stands for anticipated efforts and satisfactions, just 
as objective capital stands for anticipated services. We 
thus see in the mind of man a microcosm of the objective 
economic world, consisting of desires, efforts, and satis- 
factions, corresponding respectively in the objective world 
to capital, outgo, and income. 



Sec. 4] GENERAL SUMMARY 327 

, §4 

For convenience we have used the term "goods" to com- 
prise any one or all of the three categories, — wealth, prop- 
erty, and services. It has been seen that any two goods 
may be compared in respect to desirability, and if the 
marginal increments of two groups of goods are equally 
desirable, those groups are equivalent in value. The inter- 
equivalence of goods in this sense may be measured by ex- 
pressing all goods in terms of any one good, as, for instance, 
money. When the various goods are thus converted into 
a common standard, we have a new sense both for capital 
and income. Capital, instead of consisting of a miscellane- 
ous mass of wealth or property rights, is now taken in the 
sense of capital-value; and income, instead of consisting 
of a miscellaneous stream of services, some final and some 
intermediate, some objective and some subjective, will 
consist of a single homogeneous element, income-value. 

It is to the relation between capital and income in the 
value sense that our attention throughout this book has 
been chiefly devoted. It has been noted that the relation 
between capital and income, taken in the value sense, is 
profoundly different from the relation between capital and 
income when either or both are measured in their various 
individual units. When capital and value are measured 
as "quantities," capital maybe said to produce income; 
but when they are measured in "values," we find that it 
is necessary to reverse this statement, and to say that in- 
come produces capital. The manner in which capital- 
value is produced from income-value is by discounting, and 
this is done by means of a rate of interest, due attention 
being given to the fact that future income is always subject 
more or less to the element of chance. As a consequence 
of this fundamental discount relation, it follows that the 
value of capital rises as future income approaches, and falls 
as that income is reached and passed. It rises or falls with 



328 NATURE OF CAPITAL AND INCOME [Chap. XVIII 

each change in the rate of interest employed in the discount 
process, and with each change in the estimate of the chance 
element. If the alternate rise and fall in the value of capital 
are rhythmic and even, the capital will recur to a con- 
stant level, and the income in this case is said to be the 
earnings of capital. The earnings of capital constitute a 
standard with respect to which the actual income in any 
case may be compared. If the actual income exceeds the 
standard income, there will be a depreciation of capital, 
which may be made good, however, by paying back the 
excess into another fund of capital called the depreciation 
fund. If, on the contrary, the earnings exceed the actual 
income, the excess will constitute savings, and will accumu- 
late and be added to the capital. 

§5 

To describe in a few words the nature of capital and 
income, we may say that those parts of the material 
universe which at any time are under the dominion of 
man constitute his capital wealth ; its ownership, his capital 
property; its value, his capital- value ; its desirability, his 
subjective capital. But capital in any of these senses 
stands for anticipated income, which consists of a stream 
of services or its value. When values are considered, the 
causal relation is not from capital to income, but from 
income to capital; not from present to future, but from 
future to present; in other words, the value of capital is 
the discounted value of the expected income. The fluctu- 
ations of this capital-value will, chance aside, be equal and 
opposite to the deviations of " income" from " earnings," 
whereas, when the influence of chance is included, there 
will be in addition to these fluctuations still others which 
mirror the successive changes in the outlook for future 
income. 



GLOSSARY 

A Summary of the Definitions used in this Book 

Amortization fund. — (See Fund, depreciation.) 

Amount. — The amount of any given sum at a given time is its 

equivalent at a later time. Ch. XIII, § 1. 
Assets of a 'person. — His property-rights, including both those 
which make good his liabilities and those, if any, which 
are in excess of and free from any liability. (Syn. Resources.) 
Ch. V, § 1. 
Balance sheet. — A statement of a person's assets and liabilities. 

(Syn. Capital account.) Ch. V, § 1. 
Basis. — The rate of interest yielded by a security when sold at a 
specified price. Ch. XVI, § 9. 
commercial, of a security. — The basis corresponding to the 

commercial value of the security. Ch. XVI, § 8. 
mathematical, of a security. — The basis corresponding to the 

mathematical value of the security. Ch. XVI, § 8. 
riskless, of a security. — The basis corresponding to the riskless 
value of the security. Ch. XVI, § 8. 
Capital. — Abbreviation for Capital goods, and Capital value. 
Ch. V, § 1. 
account. — (See Balance sheet.) Ch. V, § 1. 
balance. — The difference between the value of the assets in a 
balance sheet and of the liabilities. (Syn. Net capital.) 

The capital balance is measured in three different ways: 
as the nominal capital (or capitalization), the book value, and 
the market value of the rights of the shareholders or those 
whose capital account is considered. Ch. V, § 1. 
hook value of. — The sum of the capital, surplus, and un- 
divided profits, i.e. the difference in value at any time between 
the assets and liabilities according to the entries in the capital 
account. Ch. V, § 4. 
goods. — Capital- wealth or capital-property. Ch. V, § 1. 
as market value of shares. — The market value of the share- 
holders' rights in a concern. Ch. V, § 4. 
instruments. — (See Capital wealth.) 

329 



330 NATURE OF CAPITAL AND INCOME 

Capital, net. — (See Capital balance.) Ch. V, § 3. 

nominal. — The par or face value of the shares in a joint stock 
company, and hence also the original book value of the differ- 
ence between assets and habilities. Ch. V, § 2. 

original. — The capital when the capital account is first opened. 
It may be measured in two different ways, as nominal capital 
and paid-up capital. Ch. IV, § 4, 

paid-up. — The amount of original capital of a concern actually 
paid in by the shareholders. Ch. IV, § 4. 

property. — A stock (or fund) of property existing at an instant 
of time. Ch. V, § 1. 

wealth. — A stock (or fund) of wealth existing at an instant of 
time, (Syn. Capital instruments.) Ch. V, § 1. 

value. — The value of a stock of wealth or property at an instant. 
It is found by discounting (or " capitaHzing ") the value of the 
income expected from the wealth or property. Ch. V, § 1. 
Capitalization. — A. The process of discounting by which ex- 
pected income is translated into present capital- value. Usually 
employed only when the income is considered uniform and 
perpetual, in which case capitalization consists in dividing the 
rate of income per annum by the rate of interest. Ch. IV, § 6; 
Ch. XIII, § 1. 

B. The nominal capital of a joint stock company. Ch. V, § 4. 

rate of. — The reciprocal of the rate of interest. (Theoretically 
also the reciprocal of the rate of discount. Practically this 
meaning is never used.) 
Capitalize. — To capitalize income is to find the capital-value 

equivalent to that income. Ch. IV, § 6; Ch. XIII, § 1. 
Caution, coefficient of. — The ratio of commercial value to mathemat- 
ical value. Ch. XVI, § 6. 
Chance, of any event. — The ratio of the number of cases in which 
that event may occur to the total possible number of cases, 
when all the cases are equally probable. Any two cases are 
equally probable (to any particular person at any particular 
time) if the person has no inclination to believe one rather than 
the other to be true. Ch. XVI, § 2. (Syn. Probability.) 

commercial value of. — The value which the chance will actually 
command in the market. It is equal to the mathematical 
value multiplied by the coefficient of caution, Ch. XVI, § 6. 

mathematical value of. — The product of the value of the prize 
at stake multiplied by the chance of winning it. Ch. XVI, § 5. 
Coefficient, of caution. — The ratio of commercial value to mathe- 
matical value. Ch. XVI, § 6. 



SUMMARY OF DEFINITIONS 331 

Coefjicient, of 'probability. — The ratio of mathematical value to risk- 
less value. Ch. XVI, § 6. 
of risk. — The ratio of commercial value to riskless value ; hence 
the product of the coefficient of caution multiplied by the 
coefficient of probabiUty. Ch. XVI, § 6. 

Commercial basis. — (See Basis, commercial.) 
value of a chance. — (See Chance, commercial value of.) 

Commodities. — Movable instruments not human beings. Ch. I, § 2. 

Consumption. — (See Services, enjoyable objective.) 

Couple. — A liability to a debtor and its counterpart asset to the 
creditor. Or the service of one instrument acting on another 
and the counterpart disservice of the second acted on by the 
first. Ch. VI, § 1 ; Ch. IX, § 2. 

Coupled services. — (See Couple, Interaction.) 

Depreciation fund. — (See Fund, depreciation.) 

Desirability of goods (wealth, property, or services) . — The inten- 
sity of desire, for those goods, of a particular individual at a 
particular time under particular circumstances. (Syn. Utility.) 
Ch. Ill, § 2. 
marginal — of a specified aggregate of goods. — Approximate 
definition : The desirability of one unit more or less of that 
aggregate, or the difference between the desirability of that 
aggregate and another aggregate one unit larger or smaller. 
Ch. Ill, § 4. 

Exact definition : The limit of the ratio of the increment 
(or decrement) of desirability to the increment (or decrement) 
of the aggregate when the last-named increment (or decrement) 
approaches zero. (Syn. Marginal utility.) Appendix to Ch. 
Ill, § 1. 
progressive marginal — of a specified aggregate of goods. — The 
desirability of one unit more of that aggregate. (Syn. Pro- 
gressive marginal utility.) Appendix to Ch. Ill, § 1. 
regressive marginal — of a specified aggregate of goods. — The de- 
sirability of one unit less of that aggregate. (Syn. Regressive 
marginal utility.) Appendix to Ch. Ill, § 1. 
total — of an aggregate of goods. — The difference between the 
desirability of goods which include and of those which exclude 
that aggregate. (Syn. Total utility.) Ch. Ill, § 4. 

Dimension. — The kind or species of any magnitude as indicated 
by its measurement in terms of other magnitudes. Appendix 
to Ch. I. 

Discount curve. — A curve so constructed that, if one of its ordinates 
represents any given sum, any later ordinate will represent the 



332 NATURE OF CAPITAL AND INCOME 

"amount" of that sum at a time later by an interval repre- 
sented by the horizontal distance between the ordinates ; and 
which is consequently also such that any earlier ordinate will 
represent the "present value "of that sum at a time earlier 
by an interval represented by the horizontal distance between 
the ordinates. Ch. XIII, § 1. 

Discount, rate of. — The deficiency below unity of the ratio of 
exchange between the values of present and future goods, taken 
in relation to the time interval between the two sets of goods. 
Ch. XII, § 7. 

The rate of discount may, like the rate of interest, be reck- 
oned annually, semi-annually, quarterly, or continuously. (It 
may also, theoretically, be taken in the price sense as well as 
in the sense above, but practically never is.) 
total. — The difference between any sum and its discounted or 
present value. 

Discounted value. — (See Value, present.) 

Disservice. — A negative service. An instrument renders a dis- 
service when, by its means, an undesirable event is promoted 
or a desirable event prevented. Ch. II, § 2; Ch. VIII, § 1. 

Disutility. — Negative utility. (Syn. Undesir ability.) Ch. Ill, 
§2. 

Earnings. — (See Income, earned.) 

Exchange. — The mutual and voluntary transfer of goods (wealth, 
property, or services) between two owners, each transfer being 
in consideration of the other. Ch. I, § 4; Ch. II, § 3. 

Expense. — Outgo in the form of money-spending. Ch. VIII, § 1. 

Flow. — The quantity of any specified thing undergoing any speci- 
fied change during any specified period of time. Ch. IV, § 1. 
rate of. — The ratio of a flow to its duration. Ch. IV, § 1. 

Fund. — A stock of wealth or property or its value. Ch. IV, § 1. 
amortization. — (See Fund, depreciation.) 

depreciation. — A fund formed by accumulating that part of 
income which must be turned back into capital to maintain the 
capital-value intact. It may also be defined as formed from 
the difference between real income and earnings, when that 
difference is accumulated. 

If the income is uniform and runs only for a fixed term, the 
depreciation fund may also be defined as formed from a suc- 
cession of equal payments out of income, such that if each be 
accumulated at compound interest, the total will be equal to the 
original capital at the end of the income term. (Syn. Amorti- 
zation fund.) Ch. XIV, § 6. 



SUMMARY OF DEFINITIONS 333 

Fund, sinking. — A fund formed by accumulating the difference 
between actual income and a terminable annuity which has 
the same present worth. 

As applied to bonded debts it may also be defined as 
formed by accumulating an annual sum such that its amount 
will just suffice to equal (or extinguish) a given sum at the 
end of a given period. Ch. XIV, § 7. 
Income. — Abbreviation for Income services and Income value. 
Ch. VIII, § 1. 

account. — Statement of specified income and outgo, whether from 
capital or to a person. 

earned, by any capital. — Income realized plus appreciation 
of the capital (or minus its depreciation). I.e. that income 
which a given capital can yield without alteration in its value. 
If interest be assumed invariable and all future income fore- 
known, this definition is equivalent to another, viz. the uniform 
and perpetual income which a given capital might yield; 
but the equivalence ceases if interest varies (see Appendix to 
Ch. XIV, § 1) or if future income is unknown. (Syn. Earnings, 
Standard income.) Ch. XIV, § 4. 

enjoyable. — Income which consists of enjoyable services. Ch. 
VII, § 6. 

gross. — Sum of all positive income elements. Ch. VII, § 1. 

individual. — The income from the entire capital of an individual. 
Ch. VII, § 7. 

money. — Income which consists of the receipt of money. 
Ch. VII, § 7 ; Ch. IX, § 5. 

natural. — Income which consists of services not obtained by 
exchange. Ch. VII, § 7; Ch. IX, § 5. 

net. — The difference between gross income and outgo. Ch. VIII, §1. 

psychic. — Agreeable conscious experiences. (Syn. Subjective 
income.) Ch. X, § 3. 

realized, from any capital — Actual income, i.e. the value of its 
actual services. 

services, of any capital. — The flow of services from that capital 
through a period of time. Ch. VIII, § 1. 

social. — The income from the entire capital of the society. 
Ch. VII, § 7. 

standard. — (See Income, earned.) 

subjective. — (See Income, psychic.) 

value, from any capital. — The value of its income-services. 
Ch. VIII, § 1. 
Instrument. — An individual article of wealth. Ch. I, § 1. 



334 NATURE OF CAPITAL AND INCOME 

Interaction. — An event which is a service of one capital and at the 
same time a disservice of another. (Syn. Interacting service, 
Intermediate service, Preparatory service, Coupled service.) 
Ch. IX, § 2. 
Interacting services. — (See Interaction.) 
Intermediate services. — (See Interaction.) 

Interest. — The product of the rate of interest multiplied by the 
capital-value. Ch. XIV, § 4. 
nominal. — The stipulated annual payments on a bond or note 
nominally (but not always in fact) equal to the interest on the 
"principal." Ch. XIII, § 7. 
rate of. — Many meanings are given below. The standard mean- 
ing used in this book is that called "rate of interest in the pre- 
mium sense reckoned annually." 
rate of. — In the price sense : The ratio between the annual rate 
of a perpetual annuity and the equivalent capital- value. 
Ch. XII, § 2. 

The rate of interest is said to be reckoned annually if the 
annuity is payable in annual installments; it is said to be 
reckoned semi-annually, if the annuity is payable in semi- 
annual installments; quarterly, if in quarterly installments; 
continuously, if payable continuously. 
rate of. — In the premium sense: The excess above unity of the 
rate of exchange between the values of future and present goods 
taken in relation to the time interval between the two sets of 
goods. (Syn. rate of interest in the agio sense.) Ch. XII, § 4. 
The rate of interest is said to be reckoned annually if the two 
sets of goods are one year apart. This is the standard meaning 
of the "rate of interest" as used in this book. It is said to be 
reckoned semi-annually, if they are a half-year apart; quar- 
terly, if three months apart; continuously, if infinitesimally 
apart. 
rate of. — In agio sense : (See in premium sense.) 
rate of. — Reckoned annually, semi-annually, quarterly, contin- 
uously: (See under rate of interest in price sense and rate of 
interest in premium sense.) 
total. — The difference between any sum and its "amount." 
Appendix to Ch. XIII, § 7. 
Labor. — Outgo in the form of human exertion. Ch. X, § 6. 
Land. — Wealth which is part of the earth's surface. Ch. I, § 2. 
improvements. — Wealth constructed upon and attached to land, 
Ch. I, §2. 
Liabilities of a person. — Amount of obligations due others. Ch. V, § 1. 



SUMMARY OF DEFINITIONS 335 

Mathematical basis. — (See Basis, mathematical.) 

value of a chance. — (See Chance.) 
Method, of balances. — The method of summing capital- or in- 
come-accounts which consists in first deducting the sura of 
the negative items in each from the sum of the positive items, 
and then adding the "balances" thus obtained. Ch. IX, § 2. 
of coufles. — The method of summing capital accounts and income 
accounts which consists in canceling out the "couples.' 
Ch. IX, § 2, 
Outgo. — Negative income. Ch. VIII, § 1. 

net. — Net income, when negative. Ch. VIII, § 1. 
Person. — Any owner of property, whether real or fictitious. Ch. 
II, § 3. 
fictitious. — An imaginary entity (such as a firm or corporation) 
regarded, for bookkeeping purposes, as holding property for 
a number of other persons (real or fictitious.) Ch. II, § 2. 
real. — An owner of property who is a living human being. 
Price. — A ratio of exchange. Ch. I, § 4. 

money. — The quotient found by dividing the money exchanged 
for goods by the quantity of the goods themselves. Ch. I, 
§4. 
Principal. — The final payment on a bond or note, supposed to be 
(but not always in fact) equal to the original sum " lent." 
Ch. XIII, § 7. 
Preparatory services. — (See Interaction.) 
Probability. — See Chance. 

coefficient of. — The ratio of mathematical value to riskless value. 
Ch. XVI, § 6. 
Production. — (See Transformation.) 
Productive process. — (See Transformation.) 

Productivity, physical. — The ratio of the quantity of services of cap- 
ital per unit of time to the quantity of the capital. Ch. XI, § 2. 
value. — The ratio of the value of services of capital per unit of 
time to the quantity of the capital, Ch. XI, § 2. 
Property (or property rights) . — Rights to the chance of future 
services of wealth. Ch. II, § 3. 
right, complete. — The exclusive right to all the services of an 

instrument. Ch. II, § 10. 
right, partial. — The right to part of the services of an instru- 
ment, other parts belonging to other owners. Ch. II, § 10. 
Purchase. — An exchange of money for goods. Ch. I, § 4. 
Real estate. — Land and land improvements. Ch. I, § 2. 
Resources. — (See Assets.) 



336 NATURE OF CAPITAL AND INCOME 

Return, physical. — The ratio of the quantity of services of capital 
to the value of the capital. Ch. XI, § 2. 
value. — The ratio of the value of services of capital to the value 
of the capital. Ch. XI, § 2. 

Risk, coefficient of. — The ratio of commercial value to riskless value. 
It is equal to the product of the coefficient of probability multi- 
plied by the coefficient of caution. Ch. XVI, § 6. 

Riskless basis. — (See Basis, riskless.) 

value. — The value which a thing would have if risk were elimi- 
nated. Ch. XVI, § 6. 
value of a chance. — (See Chance.) 

Sale. — An exchange of goods for money. Ch. I, § 4. 

Service. — An instrument renders a service when, by its means, a 
desirable event is promoted or an undesirable event prevented. 
(Syn. Use.) Ch. II, § 2. 

Services, coupled. — (See Interaction.) 

enjoyable objective. — Services received directly by human beings, 
and not (hke interactions) merely received for human beings 
by other objective capital. (Syn. (not well chosen) Con- 
sumption.) Ch. X, § 1. 
intermediate. — (See Interaction.) 
preparatory. — (See Interaction.) 

Sinking fund. — (See Fund, sinking.) 

Standard income. — (See Income, earned.) 

Standardize. — To standardize a given income is to convert it into 
its equivalent income earned. 

Stock. — The quantity of any specified thing at any instant. (Syn. 
Fund.) Ch. IV, § 1. 

Transaction. — That side of an exchange which relates to one of 
the exchangers ; it consists of two items, a credit and a debit. 
Ch. IX, § 9. 

Transfer. — An interaction which is a change of ownership of wealth. 
Ch. IX, § 3. 

Transformation. — An interaction which is a change of form or 
condition of wealth. (Syn. Production, Productive process.) 
Ch. IX, §§ 2, 3. 

Transportation. — An interaction which is a change of place or 
position of wealth. Ch. IX, §§ 2, 3. 

Undesir ability. — Negative desirability. (Syn. Disutility.) Ch. 
Ill, § 2. 

Utility of goods. (See Desirability.) 

Value. — ■ The value of goods (wealth, property, or services) is the 
product of their quantity multiplied by their price. Ch. I, § 6. 



SUMMARY OF DEFINITIONS 337 

Value, commercial, of a chance. — (See Chance.) 
discounted. — (See Value, present.) 
mathematical, of a chance. — (See Chance.) 
money. — The quantity of goods multiplied by their money price. 

Ch. I, § 6. 
present. — The present value of any given future goods is the 

quantity of present goods which will exchange for those future 

goods. (Syn. Present worth. Discounted value.) Ch. XIII, § 1. 
riskless, of a chance. — (See Chance.) 
Wealth (in its broader sense). — Material objects owned by 

human beings. Ch. I, § 1. 
(in its narrower sense). — Material objects owned by human 

beings and external to their owners. Ch. I, § 2. 
article of. — A single object of wealth. (Syn. Item of Wealth, 

Instrument.) Ch. I, § 1. 
item of. — (See Wealth, article of.) Ch. I, § 1. 
Worth, present. — (See Value, present.) 



APPENDICES 

Appendix to Chapter I 
Appendix to Chapter III 
Appendix to Chapter VII 
Appendix to Chapter XI 
Appendix to Chapter XII 
Appendix to Chapter XIII 
Appendix to Chapter XIV 
Appendix to Chapter XVI 



APPENDIX TO CHAPTER I 

§ 1 (to Ch. I, § 7) 

Dimensions of Wealth, Price, and Value 

What matliematicians call the "dimension" of a magnitude 
is simply its species or kind, as indicated by its measurement in 
terms of other magnitudes of the same or different kinds. It 
is expressed mathematically by a letter or letters. Consider 
beef, for example. If h represents any given amount of beef, 
say three hundred pounds, this letter may be taken to indicate 

its "dimension." The price of beef in terms of wheat is — , 



where w stands for the amount of wheat exchangeable for an 

amount h of beef. The expression — (or, as it may be written, 

h 

wb~'^) thus expresses the "dimension" of price. It matters 
not what particular price of beef in terms of wheat is referred 
to. Every price is of the same form wb~^. Finally, the di- 
mension of the " value " of the beef in terms of wheat is w, 
for this value is the product of the amount of beef, b, by its 

w . -, w 
price, — , I.e. o x~ = w. 
b b 

That is, the dimension of beef is represented by b, 
its price by jp=— =100 ^, 

its value by bp = b— = w. 

We thus have a different dimension for each of the three differ- 
ent magnitudes. This fact is expressed in common language, 
also. We measure cloth in yards, the price of cloth in bushels 
per yard, the value of cloth simply in bushels. Price and value 
differ as fundamentally as velocity and distance, which are 
measured respectively in feet per second and plain feet; or as 

341 



342 NATURE OF CAPITAL AND INCOME 

density and weight, which are expressed in pounds per cubic 
foot and simply pounds. 

It may seem at first that these distinctions between the 
dimension of price, quantity, and vahie are somewhat strained. 
It may be claimed that price is simply the value of a unit, and 
that value is simply the price of the whole quantity. In the 
same way it is sometimes loosely said that the velocity of a 
moving body is simply the distance traversed in a unit of time. 
It is quite true, of course, that the number which expresses 
the value of a unit of wealth is the same number as that which 
expresses the price per unit. It is likewise true that the 
number which expresses velocity is the same as that which ex- 
presses the distance which will be traversed in a unit of time. 
Yet velocity is not distance, and no more is price, value; although 
practically where the wealth under consideration is or may 
be regarded as a single unit, it is less necessary to insist on 
the distinction between value and price. If the price of a. 
" unique " is $25 per unit, then its value is also $25. If a farm 
of 100 acres has a value of $5000, the price of the farm as a. 
single thing, and not as measured in acres, is $5000 per farm. 

But as soon as we have to deal separately with a single unit 
and a number of units, we must make a distinction between 
price and value. That they are not of the same dimension is 
clear from the fact that the number expressing the price of 
beef in terms of wheat varies with both the unit of beef and of 
wheat, while the number expressing the value of beef varies 
only with the unit of wheat. Thus, if the quantities of beef and 
wheat which exchange for each other are 300 pounds and 60' 
bushels respectively, the price and value of the beef in terms, 
of the wheat will be 

price of the beef, | bu. per lb. 
value of the beef, 60 bu. 

A change in the unit of measurement for beef will evidently 
affect only the first of these two numbers. Thus, if the beef is 
measured in ounces (4800 oz.) instead of in pounds, the num- 
bers become : 

price of the beef, -^ bu. per oz. 
value of the beef, 60 bu. 



APPENDIX TO CHAPTER I 343 

On the other hand, a change in the unit for measuring the 
wheat will affect both numbers. Thus, if wheat is meas- 
ured in pecks instead of in bushels (while beef is still meas- 
ured in pounds), the numbers representing price and value will 
change from ^ and 60 to |- and 240 respectively, each being 
magnified fourfold. 

We see then that the value and price of beef are similar 
in that they are similarly affected by a change in the unit of 
wheat but are different in that they are differently affected by 
a change in the unit of beef. 

It may aid the reader who is unfamiliar with the subject of 
the dimensionality of magnitudes to indicate a few of its appli- 
cations to physical science. If I is taken to represent the di- 
mension of length, area will be represented by Z^ and volume 
by l^. Consequently, length, area, and volume are said to be 
respectively of one, two, and three "dimensions," because 
Z, l^, and l^, which represent their dimensionalities, have for ex- 
ponents 1, 2, and 3 respectively. The term "dimension" was 
originally applied simply to these cases of length, area, and 
volume. But it soon came to be extended to apply to every 
sort of mathematical magnitude. The following examples are 
noted without comment (I stands for length, m for mass, and 
t for time) : — 

Velocity, of dimension lt~'^, or feet per sec. 

or feet per sec. per sec. 
or pounds feet per sec. 
or pounds feet per sec. per sec. 
or pounds feet feet per sec. per sec. 
or pounds feet feet per sec. per sec. 
per sec. 

To illustrate the meaning of this table, we observe that the 
number which represents work (or energy) would be affected 
by a change in the units of mass, length, and time, as follows : 
Halving the unit of mass (so that the number representing any 
mass would be doubled) would double the number representing 
the work ; halving the unit of length (so that the number rep- 
resenting any given length would be doubled) would quadru- 
ple the number representing work ; halving the unit of time 



Acceleration, 


' It-^ 


Momentum, 


' mU~'^, 


Porce, 


'' mlt-\ 


Work, 


' mlH-% 


Horse power, 


' mlH~^, 



344 NATURE OF CAPITAL AND INCOME 

(so that the number representing any given time would be 
doubled) would quarter the number representing the unit of 
work. 

The idea of " dimension " and its mode of representation are 
important subjects, for a fuller treatment of which the reader 
is referred to the article on the subject in Palgrave's Dictionary 
of Political Econoiny, as well as for its more general applica- 
tions to J. D. Everett's C.G.S. System of Units, 1891. 

APPENDIX TO CHAPTER III 

§ 1 (to Ch. Ill, § 4) 

Definition of Marginal Desirability 

To express mathematically the marginal utility or desirabil- 
ity of any group of goods, let Aa; represent any increment of 
goods measured in any specified unit, and Am the desirability 
of that increment. For instance, if reference is had to a bin of 
coal containing 15 tons, and if Aa? represents an increment 
of 3 tons. Am will mean the desirability of those 3 tons, so 

that — will represent the average desirability per ton of 3 ad- 

Aic 

ditional tons. If we suppose the increment Aa; to be succes- 
sively decreased to 2 tons, 1 ton, i ton, and so on indefinitely, 

approaching zero as a limit, the expression — will mean suc- 
cessively the average desirability per ton of 2 additional tons, 
the desirability of 1 additional ton, the desirability per ton of 
i an additional ton {i.e. twice the desirability of that addi- 
tional half ton), the desirability per ton of \ an additional ton 
{i.e. four times the desirability of an additional ^ of a ton), 
etc. The limit of this series will be the desirability per ton of 
an infinitesimal increment of coal, and may be expressed by 

the fraction — . This, which is, as mathematicians say, the 
dx 

differential quotient of desirability, will, assuming continuity, 

have the same value if, in place of the increment, a decrement 

were considered ; that is, if instead of supposing the owner of 

the 15 tons to add 3 tons, we suppose him to subtract 3 tons. 



APPENDIX TO CHAPTER VII 345 

Then — would represent the average desirability per ton of 

Ax 

this 3 tons subtracted, which would evidently be somewhat 
greater than the desirability per ton of 3 additional tons. 
But when we substitute for 3 tons, the smaller magnitudes 

2 tons, 1 ton, i ton, i ton, etc., the resulting value of — , or the 

desirability peo' ton of this constantly lessening decrement, will 
become equal, at the limit, to the desirability per ton of the 

constantly lessening increment. The limit of — is expressed 

— . The expression — indicates more exactly than could be 
dx dx 

indicated in the text the true meaning of marginal desir- 
ability, and when the article may be indefinitely subdivided, 
the marginal desirability is the same whether reckoned 
by increments or decrements. Practically, however, such 
mathematical subdivision does not always apply, and it may 
even happen that the desirability of one unit more may be 
materially different from the desirability of one unit less. For 
instance, the owner of one piano may esteem it very highly, 
but a second piano would have almost no desirability. Here 
the desirability of one unit less is far greater than the desir- 
ability of one unit more, owing to the fact that the piano is an 
indivisible unit, and we can consider no increments or decre- 
ments except of whole pianos. In this case instead of one 
marginal desirability we have two, which may be distinguished 
as " regressive " and " progressive." 

APPENDIX TO CHAPTER VII 

§ 1 (to Ch. 7, § 1) 

Specimen Definitions of Income 

Murray, English Dictionary on Historical Principles, 1901. 

Income : 6. spec{ijically']. That which comes in as the 
periodical produce of one's work, business, lands, or invest- 
ments (considered in reference to its amount, and commonly 
expressed in terms of money); annual or periodical receipts 



346 NATURE OF CAPITAL AND INCOME 

accruing to a person or corporation ; revenue. Formerly also 
in pi. = receipts, emoluments, profits ; but the plural is now 
used only in reference to more than one person. (The prevail- 
ing sense.) 1601, E. Johnson, Kingd. & Commun. (1603) 196. 
Paying the expense of one yere with the income of another. 
1633, Herbert, Temple, Cli. Porch. XXVII. Never exceed thy 
income. 1646, H. Laurence, Oomm. Angells. 152. Hee hath 
"beene at a great deale of paines and cost; now what are his 
in-comes ? 1652, C. B. Stapylton, Herodian, 16. He scraped 
still and never was content. But studied more his Incomes to 
augment. 1697, Dryden, Virg. Georg. II, 285. No Fields afford 
So large an Income to the Village Lord. 1789, Loiterer, No. 
43, 10. Having lived, what is called up to his income, that is, 
a good deal above it. 1802, Med. Jrnl. VIII, 229. Income, in 
its usual acceptation, is a loose and vague term ; it applies 
equally to gross receipts and to net produce: But when the 
Legislature had limited it to be synonimous with profits and 
gains, it became as clear and precise as any other word. 1866, 
George Eliot, F. Holt, ii, 1, 76. No, I shan't attack the Church — 
only the incomes of the bishops, perhaps, to make them eke 
out the incomes of the poor clergy. 

These definitions afford no means of deciding on net income. If in- 
come is simply what comes in and outgo simply what goes out, and if in 
any year as much passes out of one's hands as comes in, is the net income 
izero? 

Dr. N. G. Pierson, Principles of Economics Trans, by A. A. 
Wotzel, Vol. I, p. 76. London (Macmillan & Co.), 1902. 

By social income we mean the sum-total of economic goods 
which a nation has at its disposal in a given period of time; 
the net result of the productive labour of the nation during that 
time. 

Is not its capital " at its disposal " in any period ? Is it then income ? 

Eoscher, Principles of Political Economy (2d vol., Eng. trans., 
p. 5), speaking of national wealth, says that gross income con- 
sists of, — 

"■ (a) Of the raw material newly obtained in the country. 

" (6) Of imports from foreign countries, including that which 
is secured by piracy, war booty, contributions, etc. 



APPENDIX TO CHAPTER VII 347 

" (c) The increase of values which industry and commerce 
add to the first two classes up to the time of their 
final consumption. 

" (d) Services in the narrower sense and the produce of 
capital in use. 

" To find the national net income we must deduct the follow- 
ing items : — 

"(a) All the material employed in production which yields 

no immediate satisfaction to any personal want. 
" (6) The exports which pay for the imports. 
" (c) The wear and tear of productive capital and capital in 

use." 

The method thus illustrated is the method which takes its 
starting point from the goods. There is another method which 
takes its starting point from the persons who receive them. 
By this method the national income is to be calculated as 
follows : — 

"(a) From the net income of all independent private busi- 
nesses, etc, 
" (b) From the net income of the state, of municipalities, 
corporations and institutions, derived from their 
own resources. 
" (c) Under the former heads must be taken into the account 
such parts of property as have been immediately 
consumed and enjoyed. 
"(d) Interest on debt must be added only on the side of 
the creditor and deducted from the income of the 
debtor." 

How is double counting to be avoided if " raw materials produced" 
(a) are income and also "the produce of capital in use" (d)? "Increase 
of values" (c) is not income but capital. 

Alfred Marshall, Principles of Economics, Vol. I, pp. 149, 150. 
London (Macmillan), 1898. 

"Another convenient term is the usance of wealth. It means 
the whole income of benefits of every kind which a person 
derives from the ownership of wealth, whether he uses it as 
capital or not. Thus it includes the benefits which he gets 



348 NATURE OF CAPITAL AND INCOME 

from the use of his own piano, equally with those which a 
piano dealer would win by letting out a piano on hire. 

" This income is most easily measured when it takes the form 
of a payment made by a borrower for the use of a loan for, 
say, a year ; it is then expressed as the ratio which that pay- 
ment bears to the loan, and is called interest. But this term 
is also used more broadly to represent the money equivalent to 
the whole income which is derived from capital. 

* * * * # * * 

"Social income may be estimated by adding together the 
incomes of the individuals in the society in question, whether 
it be a nation or any larger or smaller group of persons. 
Everything that is produced in the course of a year, every serv- 
ice rendered, every fresh utility brought about is a part of the 
national income. 

"We must be careful not to count the same thing twice. 
If we have counted a carpet at its full value, we have already 
counted the values of the yarn and the labour that were used 
in making it ; and these must not be counted again. But if 
the carpet is cleaned by domestic servants or at steam scouring 
works, the value of the labour spent in cleaning it must be 
counted in separately ; for otherwise the results of this labour 
would be altogether omitted from the inventory of those newly- 
produced commodities and conveniences which constitute the 
real income of the country." 

"Usance of wealth" is apparently identical with income as explained 
in this book. "Social income," however, seems at variance with the 
concept of " usance " ; for it includes concrete wealth. 

William Smart, The Distribution of Income, London (Mac- 
millan), 1899, p. 18. 
"In any case, the attempt at classification seems to bring 
out clearly that there are, conceivably, two ways of computing 
the real National Income : the one which takes it as the sum 
of consumption goods plus any additions to capital, the other 
which takes it as the sum of the services which contribute 
to the making of them ; and that these two are alternatives. 
Either alternative, however, may be used when different pur- 
poses are in view ; and the thesis which I put forward is that. 



APPENDIX TO CHAPTER VII 349 

while the National Income must be conceived of as the total 
sum of consumption goods, as these and these alone are the 
means of satisfying the end of economic action, the life of man, 
it must be calculated as the sum of the contributory services." 
Includes concrete goods and abstract services. 

F. W. Taussig, Wages and Capital (Appleton & Co., New 
York), 1906, p. 36. 

^' It would seem best, therefore, to let the term capital stand 
simply for inchoate wealth : for all the possessions that do not 
yet serve human wants. Tools and machines, factories and ware- 
houses, raw materials and half-finished and nearly finished 
goods, — these all go together as being not directly conducive 
to enjoyment; while all forms of finished commodities — food, 
houses, clothes, ornaments — belong together as enjoyable 
wealth and as income." 

Are houses income ? 

Henry Rogers Seager, Introduction to Economics (Holt & Co., 
New York), 1904, pp. 163-164. 
"The money income is merely the convenient medium by 
means of which the real income of the community is divided 
among those entitled to share it. This real income consists of 
consumable goods for those who spend their entire money 
incomes, and partly of consumable goods and partly of capital 
goods for those who save." 

As to the inclusion of "savings" under Income, see text of this chapter 
and the fuller treatment in Chapter XIV. 

Charles Jesse Bullock, Introduction to the Study of Economics, 
rev. ed. Boston (Silver, Burdett & Co.), 1900, p. 376. 

"In this way the social income for any month or year may 
be divided into four constituent parts : — 

"1. The satisfactions derived from durable consumable goods, 
the product of past industry, that still remain in the possession 
of the community and add to its material enjoyments. 

"2. The personal services at the disposal of the society dur- 
ing the period for which the income is computed. 

"3. The material goods of a consumable character that are 
the product of the current industry for the period considered. 



350 NATURE OF CAPITAL AND INCOME 

"4. The producers' goods, or capital, created by the current 
industry of the period, and available for the production of 
economic goods during the following periods." 

Is double counting avoided ; e.g. Are material goods to be counted, and 
then, in addition, the satisfactions from them ? 

Frank A. Fetter, Tlie Principles of Economics, New York (The 
Century Co. ), 1904, pp. 40, 41. 

3. " Objective income consists of the additional sums of goods 
acquired by individuals or by society during the income period. 

TV tF ^ ^ ^ ^ :^ 

4. " Income in the logical sense must be a net addition, but the 
term gross income is not loithout popular and practical meaning. 
Gross income is sometimes spoken of in the sense of total 
receipts, as the total of goods secured; net income is the re- 
mainder after deducting expenditures and after replacing the 
goods employed to secure the income. In order to produce 
some goods technically, men make use of other goods. While 
they are storing up a supply of wood or coal it may be looked 
upon as the income, but they may burn it to help grow hot- 
house plants. While they gather flowers with one hand, they 
destroy fuel with the other. Only the net increase in value 
can be accounted income in the second period. The goods 
that come into a man's possession in any period are of many 
sorts : to get some he has destroyed many previously existing 
goods; while to get others he has not needed to use up the 
accumulations of the past or to mortgage the future. The one 
kind is gross, the other net income. 

5. ^^ An income of consumption goods is a part of wealth, but 
not the whole of it. The consumption goods, the 'present 
goods' at the moment available, are the essential part of 
wealth for the moment's enjoyment. The only essential and 
immediate conditions of a series of gratifications is a regular 
series of consumption goods. But many things existing which 
could be used to secure a gratification are not in fact treated 
as consumption goods. A crop of corn is not all income. In 
a time of famine it could be used, but seed-corn was saved from 
last year, and some must be kept for next year. This is a 



APPENDIX TO CHAPTER VII 351 

part of wealth, but not of 'present goods' as we understand 
the term." 

" Goods " are not income. Increase of value is not income. See text. 

Kleinwachter, Das Einkommen und seine Verteilung, Leipzig, 
1896, pp. 11, 12. 

So bestimmt beispielweise das Einkommensteuergesetz flir 
Hamburg vom 26. Marz, 1886, im Sec. 4: — 

"Die Einkommensteuer ist von dem reinen Einkommen oder 
Erwerb zu entrichten, d. h. alien in Geld oder Geldeswert 
(etwaige selbstverwohnte Miete, den Wert etwaige freier 
Wohnung, Naturallieferungen u. s. f. hinzugerechnet) beste- 
henden Einnalimen des Steuerpflichtigen, ohne Ausnahme, 
gleichgiltig aus welcher Quelle sie gefiossen. . . ."^ 

Ahnlich sagt das sachsische Einkommensteuergesetz vom 2. 
Juli, 1878, im § 15: — 

"Als Einkommen gilt die Summe aller . . , Einnahmenmit 
Einschluss des Mietwertes der Wohnung im eigenen Hause, 
sowie des Wertes der zum Haushalt verbrauchten Erzeugnisse 
der eigenen Wirtschaft. . . ." 

Und fast mit denselben Worten, nur etwas minutioser und 
genauer, sagt der osterreichische Entwurf eines Gesetzes, 
betreffend die direkten Personalsteuren vom Jahre 1892, im 
§195: — 

"Als Einkommen gilt die Summe aller in Geld oder Geldes- 
wert bestehenden Einnahmen der einzelnen Steuerpflichtigen 
mit Einschluss des Mietwertes der Wohnung im eigenen Hause 
oder sonstiger freier Wohnung, sowie des Wertes der zum 
Haushalte verbrauchten Erzeugnisse der eigenen Wirtschaft 
und des eigenen Gewerbebetriebes, sowie sonstiger dem 
Steuerpflichtigen allenfalls zukommender ISTaturaleingange." 

Bemerkenswert ist, dass keine dieser Gesetzesstellen die 
einzelnen Arten oder Zweige oder Bestandteile des Einkom- 
mens, die der Steuer unterworfen sein sollen, taxativ aufzahlt, 
sondern dass die in Eede stehenden Gesetze das "Einkommen" 
ganz allgemein zu definieren bestrebt sind. Und der Tenor ist 
jedesmal : " Unter Einkommen versteht man alle in Geld oder 



352 NATURE OF CAPITAL AND INCOME 

Geldeswert bestehenden Einndhmen, gleichgiltig aus welcher Quelle 
sie gejiossen.'' Da nun in unserer heutigen auf der Grundlage 
des Privateigentums und der Individualwirtschaft aufgebauten 
Volkswirtschaft 

1. alle erdenklichen Sachgtiter, 

2. alle erdenklichen Nutzungen dieser Sachgiiter und 

3. alle erdenklichen personlichen Dienstleistungen um Geld 
verkauft und gekauft werden konnen und demgemass " Geldes- 
wert haben," so ergiebt sieh, dassder Gesetzgeber alle materiel- 
len und immateriellen Gliter, die in die Wirtschaft des 
Einzelnen treten, unter den Begriff des Einkommens sub- 
sumiert wissen will. . . . Das heisst also mit anderenWorten: 
der Gesetzgeber definiert den Einkommensbegriff in der nam- 
lichen Weise, wie es oben definiert wurde, und zwar so, dass 
unter "Einkommen" alle Giiter verstanden werden sollen, 
welcbe entweder in die eigene Wirtschaft von aussen her- 
einkommen, oder welche innerhalb der eigenen Wirtschaft neu 
entstehen, und zwar gleichgiltig ob diese Giiter materielle (oder 
Sach-) Giiter, oder ob sie immaterielle Giiter (d. i. Nutzungen 
von Sachgiitern oder personliche Dienstleistungen) sind. 

To include in income all newly acquired or newly produced goods is 
clearly to include too much. To restrict income to money receipts is, as 
shown in the text, to err both in inclusion and exclusion. To require that 
the income shall be "rein" or "net" without defining the deduction 
required to make it so is to leave the definition incomplete. 

Kleinwachter, op. cit., pp. 22-23. 

An dieser Stelle gentigt die Bemerkung, dass die Hek- 
MANN-ScHMOLLEBSCHE Definition oder Auffassung des 
(Einzel-) Einkommens bis auf den heutigen Tag so ziemlich 
(die abweichenden Meinungen sollen welter unten erwahnt 
werden) die herrschende geblieben ist. Hermann (" Staats- 
wirtschaftliche Untersuchungen." 2. Aufl., Miinchen, 1870, 
S. 582 u. 583) definiert das (Einzel-) Einkommen wie folgt: 

"So wenig jede Ausgabe Verbrauch ist, so wenig ist jede 
Einnahme Einkommen. Dieses ist vielmehr die Summe der 
wirtschaftlichen oder Tauschgiiter, welche in einer gewissen 
Zeit zu dem ungeschmalert fortbestehenden Stammgut einer 
Person neu hinzutreten, die sie daher beliebig verwenden kann. 



APPENDIX TO CHAPTER VII 353 

Dass es ebensowohl korperlicher als unkdrperlicher Natur sein 
konne, ist klar." 

Und im Anschlusse an diese Hermannschb Definition des 
Einkommens sagt Schmolleb ("Die Lehre vom Einkommen 
u. s. w." in der "Zeitschr. f. d. ges, Staatsw. " Jalirg. 1863, 
Bd. 19, S. 1 ff. speciell S. 19): — 

" Einkommen ist . . . also die Summe von wirtschaftliclien 
Giitern, die ein Subjekt in einer gewissen Zeit zur Befriedigung 
seiner Bedlirfnisse ohne Schmalerung seines Vermogens ver- 
wenden kann. Filr Jeden sind die Frilclite seiner Arbeit und 
seines Vermogens sein ursprtingliches Einkommen; ein ab- 
geleitetes hat nur der, welcher solcbe Ertichte nicht hat ; d. h. 
nur er lebt vom Einkommen anderer. . . . Zum Einkommen 
gehoren stets aiich samtliche unmittelbar, d. h. ohne Tausch, 
verbrauchten oder genossenen Ertichte der Arbeit und des 
Vermogens." 

The foregoing definitions express in a general way wiiat we have called 
" earnings " as distinct from " income." They err however by fixing on 
concrete commodities in place of their services and in some other respects. 
See text. 

In erschopfender Weise hat Adolf Wagner die aus der 
bisher geschilderten Auffassung entspringenden Einkommens- 
definitionen in seiner bekannten "Grundlegung" (1. Aufl., S. 96 
u. 97 ) zusammengefasst, wenn er das Einzelneinkommen defin- 
iert wie folgt: — 

"Im Einkommen (einzeln in den Einktlnften) werden die 
Einnahmen oder Ertrage in Beziehung mit der Person, welche 
sie empfangt, daher mit dem Wirtschaftssubjekte gebraeht. 
Das Einkommen einer Person umfasst zweierlei: — 

"1. Diejenige Summe wirtschaftlicher Giiter, welcher der- 
selben in gewissen Perioden . . . regelmassig und daher mit 
der Fahigkeit der regelmassigen Wiederholung als Eeinertrage 
einer festen Erwerbsquelle neu als Vermogen hinzuwachsen. 
Dieser Teil des Einkommens einer Person rilhrt daher aus der 
Wirtschaftsfilrung ilberhaupt und aus einzelnen wirtschaft- 
lichen Thatigkeiten (Arbeit, Unternehmung) oder aus Eigen- 
tums- oder Eorderungsrechten inbesondere (Sklaveneigentum, 
Grundeigentum, Kapitaleigentura, Eorderungen aus Kreditge- 
2a 



354 NATURE OF CAPITAL AND INCOME 

schaften), endlich aus regelmassigeu unentgeltlichen Ein- 
nahmen (Almosen, Geschenk) her. 

"2. Die Gentisse (JSTutzungen) oder selbst nur die Genuss- 
moglichkeiten, welche das ISTutzvermogen einer Person nach. 
Abrechnung der dabei stattfindenden Abnutzung und Verkehrs- 
wertverminderung periodisch. fortdauernd gestattet. 

" Das Einkommen einer Person bildet zunacbst den Giiterf end 
zur Befriedigung ihrer Bedtirfnisse. Seine Erwerbung ist das 
Mittel zu letzterem Zwecke. Es kann in derselben Periode, 
in der es erlangt wurde, vollstandig verzehrt werden, ohne dass 
dadurch das frtihere Vermogen geschmalert wird. Die Tausch- 
werthohe des Einkommens einer Person entsclieidet liber das 
Mass der letzterer moglichen dauernden Bedilrfnisbefriedigun- 
gen, ist daher volkswirtscliaftlich von grosster Bedeutung." 

The errors in Wagner's definition are the restriction that income must 
be "regular" and the inclusion of concrete commodities and abstract 
services, side by side. 

Kleinwachter, op. cit., p. 24. 

. . . man heute unter dem Einkommen einer Person ver- 
steht : — 

alle Guter, welclie in die Wirtschaft oder in das Vermogen 
einer Person treten, und zwar : — 

1. gleichgiltig, ob diese Gilter von aussen in die eigene 
Wirtschaft hereinkommen, oder ob sie innerhalb der eigenen 
Wirtscliaft neu entstanden sind, und 

2. gleicbgiltig, ob diese Gtiter materieller oder unmateriel- 
ler Natur sind. 

Allerdings mtissen in diese Definition zwei weitere Momenta 
aufgenommen werden, wenn dieselbe die heutige communis 
opinio der Wissenschaft widerspiegeln soil, zwei Momente, die 
ich in der "Einleitung" mit Vorbedacht unberticksichtigt 
gelassen babe, well sie ftir den mir dort vorscbwebenden Zweck 
bedeutungslos waren, namlich : — 

1. dass die in Rede stehenden Gtiter mit einer gewissen 
Eegelmassigkeit in die Wirtschaft oder in das Vermogen der 
betreffenden Person treten milssen, wenn sie als " Einkommen " 
gelten sollen, und 

2. dass diese Gtiter nur dann als "Einkommen" aufgefasst 



APPENDIX TO CHAPTER VII 355 

werden konnen, -vvenn sie neu in die Wirtschaft oder in das 
Vermogen der betreffenden Person treten, d. h. also wenn sie 
zu dem bislierigen Vermogen der betreffenden Person hinzu- 
treten, oder mit anderen Worten: es liegt umgekehrt kein 
"Einkommen" vor, wenn Guter in die eigene Wirtschaft her- 
einfliessen, welche Teile des Stammvermogens dieser Wirtschaft 
sind, also beispielweise, wenn ausstehende Forderungen zu- 
riickgezalilt oder ausgeliehene Vermogenobjekte zurtickgestellt 
werden. 

According to Kleinwachter the effort to reach a self-consistent concept 
of income had led to the inclusion of every element flowing into one's 
possession whether by exchange from without or by production from 
within his own establishment, and whether these elements are material or 
immaterial, so long as we exclude such elements as " irregular " receipts 
and the return of old debts. The uselessness of such a concept Klein- 
wachter himself points out. 

Eobert Meyer, Handioorterhucli der Staats- Wissenschaften, Bd. 
Ill, Art. Einkommen "Begriff," p. 348. 

Die englische liberale ISTationalokonomie war von dieser 
Grundlage aus zu einseitigen Eesultaten gelangt, indem sie das 
Einkommen ganz in der Art verstand, wie die Buchhaltung 
einer kaufmannischen oder industriellen Unternekmung den 
Eeingewinn ermittelt. 

M, M, M, ^ ^ ^ M, 

TT ■VT -TS" TT •R" TV" ■TV' 

Die deutscke Litteratur hat diese Einseitigkeit vermieden, 
und die bis auf die Gegenwart herrsckend gebliebene Her- 
mannsche, von Schmoller erganzte und vielleickt tlber Gebiihr 
viel bewunderte Lehre versteht unter Einkommen alle Tausch- 
giiter, die nach vollstandiger Herstellung alles Stammver- 
mogens innerhalb des Jahres neu erzeugt und dargeboten 
werden und zur Befriedigung der Bedtirfnisse der Nation 
dienen raogen (Hermann), oder die Summe der wirtschaftlicken 
Guter, die ein Subjekt in einer gewissen Zeit zur Befriedigung 
seiner Bediirfnisse ohne Schmalerung seines Vermogens wer- 
wenden kann (Schmoller) . 

^ -TT tP T? ^ TT tP 

In neuerer Zeit ist ein frtiher als selbstverstandlich vor- 
ausgesetztes Merkmal auch begriflich in den Vordergrund 



356 NATURE OF CAPITAL AND INCOME 

gestellt -worden: die Wiederkehr, die regelmassige Wieder- 
kehr oder die Fahigkeit der Wiederkehr der das Einkommen 
bildenden Einnahmen. 

Formliclie Definitionen des Einkommens werden haufig 
vermieden, doch sagt die sachsische Einkommen steuer vom 2. 
Juli, 1878, § 25: Als Einkommen gilt die Summe aller in 
Geld und Geldeswert bestehenden Einnahmen abztlglich der 
auf Erlangung, Sicherung und Erhaltung dieser Einnahmen 
verwandten Ausgaben sowie etwaiger Schuldzinsen, auch in- 
sofern diese nicht zu den eben bezeichneten Ausgaben gehoren, 
Ausserordentliche Einnahmen durch Erbschaft und ahnliche 
Erwerbungen gelten jedoch nicht als steuerpflichtiges Einkom- 
men, sondern als Yermehrung des Stammvermogens. Ganz 
ahnlich das osterreichische G. v. 25. Oktober, 1896, welches 
jedoch den zweiten Absatz anders gefasst hat: — 

"Ausserordentliche Einnahmen aus Erbschaften, Lebens- 
liapitalsversicherungen, Schenkungen und ahnlichen unentgelt- 
lichen Zuwendungen gelten nicht als steuerpflichtiges Ein- 
kommen. " 

These formulations virtually repeat the definitions given above. 

Eranz Guth, Die Lehre vom Einkommen in dessen Qesammt- 
zweigen, Leipzig, 1878, p. 62. 

Einkommen ist jede aus einer Quelle, also mit einer gewissen 
^egelmassigkeit widerkehrende Vermehrung des Verm o gens. 
Der Bezieher Kann es geniessen, verzehren, oder auf irgend 
•einer Art vernichten, ohne seinen Eonds zu schwachen. Lot- 
teriegewinne, precare Almosen und Geschenke sind daher kein 
Einkommen, wohl aber sind es Almosen und Geschenke, die 
sich auf gewisse Titel griinden. 

This view is discussed iu the text. 






APPENDIX TO CHAPTER XII 357 

APPENDIX TO CHAPTER XI 

§ 1 (to Ch. XI, § 2) 

Dimensions of Income-capital Ratios 

If we indicate time by t and distinguish the quantity and 
value of services by the letters q and v, and the quantity and 
value of capital by Q and V, the four ratios mentioned assume 
the form : — 

Physical productivity, -^, e.g. bushels per acre per year. 

Yalue productivity, — , e.g. dollars per acre per year. 

Physical return, -^, e.g. bushels per dollar's worth of 

capital per year. 

Talue return, — , e.g. dollars per dollar ( i.e. per cent) 

per year. 

APPENDIX TO CHAPTER XII 

§ 1 (to Ch. XII, § 2) 

-Mathematical Relations between Rates, Annually, Semi-annually, etc., 
when conceived in the Sense of the Price of Capital 

If i' represents the rate of interest per annum when the 
income is payable semi-annually (such as 4 % in the example 
in the text) and i the rate which would be its equivalent when 
the income is payable annually (such as 4.04 <fo in the example), 
the relation between V and i is, — 

4 

To show this we observe that under our hypothesis as to i 

and i', a capital of f 1 will buy a perpetual income of either i 

V 
■each year, or - each six months. Let us suppose, as in the 

preceding example, in six months the holder of the latter 

i' 
annuity, after receiving his first installment of income, „? sells 



358 NATURE OF CAPITAL AND INCOME 

out for $1, which he may evidently do if the rate of interest 

i' 
remains unchanged. With his total receipts, 1 + -, he buys a 

new annuity of the same type. This will evidently yield him 
1 + M i' per annum, payable in semi-annual installments of 

half that amount, or ^^ — jr-^ — . At the end of another six 

Zi 

months, then, he receives this last-named sum, and, selling his 

i' . 

newly bought annuity for its original value of 1 + -, he has in 

i' (^ + 5)'-' 

hand a total sum of l + --f ^ ^ — Of this sum he rein- 
vests $ 1 and retains as income the remainder, or - -f 



2 ' 2 

This sum may evidently be obtained year after year simply 
by repeating the above process. It constitutes a perpetual 
annuity, payable annually, and its value simplified from the 

above formula is evidently %'-{-—. 

Since this is the annual income, payable annually, which f 1 
of capital will hwj, it is by definition, the magnitude we called i; 

that is, i = i' -f - . 
4 

We may in like manner proceed to quarterly payments, in 

which case we shall find, by analogous reasoning, denoting by 

i" the rate of interest per annum payable quarterly, that 

8 ^16 256 

§ 2 (to Ch. XII, § 4) 

Mathematical Relations between Rates reckoned Annually, Semi-annually, 
etc., when Rates are conceived as " Premiums." Diagrammatic Rep- 
resentation. Economic Interpretation of e. 

In general let i' be the rate of interest per annum reckoned 
semi-annually. Then the " amount " of f 1 in six months is 



APPENDIX TO CHAPTER XII 359 

i' 
1 + - , and this sum in another six months will " amount " by 

compound interest to 1 1 + - J , which must be equal to 1 + i, 

the " amount " of $1 in one year at the equivalent rate of inter- 
est, i, reckoned annually; i.e. 

or, expanding and reducing, — 

1 = 1'+-, 

4 
which is the same result obtained before when the rate of 
interest was regarded as the price of capital. 

Similarly, for the interest rate i", reckoned quarterly, we 

may prove 1 -\- i = (1 -\ j , and for the interest rate i^"', 

reckoned n times a year, 1 -\- i —11 -\ )• 

V ^ J 

In other words, 

^H i" 
= 1^+4 



= fl + 

n 



■^(.n)\n 



o (n)\ J!L 

n 



■(n) 



As n increases indefinitely, the last expression approaches a 
limit. The limit of i'-"^ is the " rate of interest per annum com- 
puted continuously," called S. The limit of the square bracket 
is the base of the Napierian system of logarithms called e ; for 

by the definition of e usually given, it is the limit of ( 1 + - j, 

when k is any number increasing indefinitely. Evidently 

-; — is such a number, for n, by hypothesis, is to be increased 

indefinitely, and i^"-'' evidently decreases. Hence at the limit 
the last formula becomes, 

1 + i = e« ; 
Or, substituting for e its numerical value, 
1 + I = (2.7182818)«. 
Another proof of this formula could be given for the case 
where the rate of interest is conceived as the price of capital, 



360 NATURE OF CAPITAL AND INCOME 

by following to the limit the method of this Appendix, § 1 
above. 

The number e, or 2.7182818, plays almost as important a role 
in mathematics as the number 3.141592, called ir, which 
expresses the ratio of the circumference of a circle to its diam- 
eter, but the meaning of e is less familiar to most students. 
Various definitions and interpretations may be given. To the 
economist, the most interesting is the following: e is the 
"amount" of fl put at compound interest during the "pur- 
chase period," the latter being derived on the assumption that 
the rate of interest is payable continuously. 

This proposition is implicitly contained in the demonstra- 
tion of the equation 1 -\-i= e^, as given above. The following 
is a more explicit statement, with actual illustrative figures : — 

If we consider the rate of interest 4%, or - — - payable 

annually, the purchase period is 25 years, or , and the 

amount of f 1 put at 4% interest for these 25 years will be 

(1 + .04)25. 

If next we take 4% payable semi-annually, the 
amount of $1 during the purchase period of 25 f^ .04V 
years will be \ 2 J 

Similarly, the amount of $1 put at interest at /-. .04 V 
4% payable quarterly is \ 4 y 

And if the interest is reckoned as payable w /-. .04\-^ 
times a year, the amount is \ n J 

At the limit, we have the amount of $1 at interest at 4^ 
for 25 years when the rate of interest is payable continuously. 
The limit of the above expression, when n is made indefi- 
nitely great, is the definition of e. 

The distinction between the different rates of interest may 
be shown by a diagram. In Figure 33, let the curve B'AB rep- 
resent a "discount curve," any two ordinates of which represent 
exchangeable goods situated at two corresponding points of 
time, as a and b, that is, the sum aA of " present " goods will buy 
the sum bB of goods which lie in the future a time interval ab, 
beyond the " present." If we take these two points, a and b, a 
year apart, the rate of interest as reckoned annually is the 



50 



100 



APPENDIX TO CHAPTER XII 



361 



"slope" of the secant AB in relation to the ordinate aA 
—=^ -5- aAy Similarly, the- slope of the secant AC drawn 

through points corresponding to times a half year apart, taken 
in relation to aA, is the rate of interest reckoned semi-annually. 




Fig. 33. 



and so on. At the limit, the slope of the tangent AT (in re- 
lation to aA) represents the rate of interest reckoned continu- 
ously. 

Similarly, the regressive secant, AB', represents the rate of 
discount, reckoned annually (if ab' represents a year interval), 



362 NATURE OF CAPITAL AND INCOME 

AC, the rate reckoned semi-annually, and so on until the tan- 
gent AT',OT AT, is again reached, when the distinction between 
interest and discount disappears. It is easy to prove (by simi- 
lar triangles) that the reciprocal of the rate of interest continu- 
ously reckoned, in other words the "year's purchase," is 
represented by aS the subtangent. 

§ 3 (to Ch. XII, § 6) 

A Fremium Rate of 4% one Year and 3% Each Year after means a Price 
Rate of 3.03% the First Year. 

We have given 4% as the rate of interest (as premium) in 
the first year, and 3 % as the rate for each year thereafter. 

Let us suppose that f 100 to-day is invested for $ 104 next 
year, and that at the end of the year, of this $ 104, f 100 is re- 
invested. Since thereafter the rate of interest is always 3% 
in the premium sense, it must be, by proof in the text, also 3% 
in the price sense. Consequently, the $100 reinvested next 
year may be used to buy $ 3 a year forever. The result is that 
for the $ 100 to-day the return is f 4 next year and $ 3 each 
year thereafter. This series of payments is the same as $3 a 
year forever, together with one extra dollar at the end of the 
first year. This extra dollar has a present worth (since the 
interest premium between this year and next year is 4%) of 
-i-, or .96j\. If we deduct this present value of the extra 
dollar from the $100 (which is the present value of the entire 
series of $4, $3, f 3, $3, etc., ad inf.), we have the present 
value of the series without the extra dollar, i.e. of $3 a year 
forever. The remainder is $99.03^. Since, then, this 
$99,031^ will buy f 3 a year forever, the rate of interest in the 
pnce sense is $3-j-$99.03i|, or 3.03% approximately. This 
is the rate at the outset. After the first year it will evidently 
always be 3%. 

§ 4 (to Ch. XII, § 6) 

A Price Rate of 4 % this Year and 3 % Each Year after means a Premium 
Rate of 371% the Eirst Year. 

We have given 4 % as the rate (in the price sense) for the 
first year, and 3% as the rate (in the same sense) for each year 
after. 



APPENDIX TO CHAPTER XII 363 

$ 100 will to-day buy the right to $ 4 a year forever, and a 
year hence this right to $4 annually may be sold on a 3% 
basis. It will therefore fetch $ 133.33. The investor will 
consequently receive in all, at the end of this first year, a total 
of 14+ f 1331 or f 1371. Hence the rate of interest in the 
sense of a premium will be for that year 37-^%. In succeed- 
ing years the rate of interest, considered either as a premium or 
a price, will evidently be 3%. 

§ 5 (to Ch. XII, § 6) 

Mathematical Kelations between the Rates of Interest as a Premium and 

as a Price 

In general, if we let ii represent the rate of interest in the 
premium sense for this year, Zg for next year, ig for the third 
year, and so on, whereas ji,J2, and jg, etc., represent the 
rates of interest in the price sense for the same successive 
years, the following relations between the i's and /s may be 
proved: — 

+ ,H , .., +7:; r-T-+ . • • ad inf. = 



^ - + 7 — -v^ -\ : ^"^—^ : — h ... ad inf. 



1 + i, (1 + ii)(l + Q (1 + h) (1 + *2)(1 + ^'3) 
^-+ .. ^ ... + ,. ^. .., + . . . ad inf. = 



1+J2 (i+j^y (l+i^/ 

^ + 73 A ^ +^. .... "^ ■ w. rT-+ ... ad inf. 



1 + i^ (1 + i,)(l + Q (1 + i,)(l + g (1 + ii) 

etc. 

These equations may be said to determine j^, as a peculiar 
sort of mean of the magnitudes ii, i^, h, . ■ • ad inf., and J2 as a 
similar mean of {2, 4, U, ... ad inf., etc. Their proof, 
which is simple, is left to those readers who are interested in 
mathematics. 

The preceding equations express the values of the /s in 



.04 + -^^ 7^-^^ = .371 



364 NATUKE OF CAPITAL AND INCOME 

terms of i's. The following equations give the i's in terms of 
the /s : — 

h 

h 

''5—jz T : J 

Ji 

etc. 

Thus if, as in our example, ji = .04 and j^ — .03, 

.04 - .03 
.03 

The proof of these formulae is also left to the mathematical 
reader. He will observe that the two sets of equations may be 
proved independently or either set may be proved and the 
other set derived from it. To show that either set may be de- 
rived from the other, it will be found useful to substitute for 
the left-hand members of the first set their simpler values as 

111 

derived by algebra. These are, -, r^-, etc. An easy proof of 

Jl J'2 Jz 

this is found by actually dividing 1 by Ji, etc. 

From the formulae it is clear that if ii= t2= ^'3=, etc., then 
j.^=J2=J3=, etc., and that then all the t's = the /s. The 
converse is also evident. 

§ 6 (to Ch. XII, § 7) 

Mathematical Kelations between the Eates of Interest and Discount 

Let V, due one year hence, be the equivalent of V available 
in the present. Then the rates of interest and discount are 
expressed respectively by the formulae : — 

l + i = ^; 

l-d = Z. 

V 

Whence, by multiplying the two equations together we 
derive (1+0 (1 — d) = l, which reduces to d = i — id. That 
is, the number representing the rate of discount equals the 
number representing the equivalent rate of interest less a 



APPENDIX TO CHAPTER XII 365 

small correction, equal to the product of the rates of interest 
and discount. 

The relation between the rates of discount and interest 
when semi-annually reckoned is analogous to the relation which 
we found between those annually reckoned. We then have 

the equations, — = 1 — — - 

V Z 

and Y = ^-2' 

^Hence (^1_|:) (l + |') = l. 

By multiplication and reduction, 

We may apply similar reasoning to quarterly-reckoned 
interest and discount rates. 

It follows that ( 1 + J ) (^ - x) = 1' 

or d" = i"-''-^. 

4 

The same reasoning may obviously be applied to reckonings 

n times a year. We then find, 

n 
It is evident that if n, the number of parts into which the 

year is divided, be sufficiently increased, the term be- 
comes infinitely small, so that, at the limit, the rate of interest 
and the rate of discount become equal. This rate for continu- 
ous reckoning, being the same as the rate of interest for con- 
tinuous reckoning, is also called 8. 

Unlike the rate of interest, the rate of discount is always 
considered as associated with the exchange of present against 
future goods, and not with the exchange between capital and 
income, i.e. is taken, not in the "price" sense, but in the "pre- 
mium" sense (the premium being, in this case, negative). We 
may, however, to complete our scheme of concepts, construct 
for ourselves a "rate of discount" in the sense of the price of 
capital in income. We recur to the fact that the rate of 



366 NATUKE OF CAPITAL AND INCOME 

interest, in the price sense, was defined as the ratio of 
income to capital, when the first installment of income is 
due at the end of the first time-interval. But if the first 
installment is due at the beginning, the ratio of income to 
capital is no longer the rate of interest, but may be called a 
sort of rate of discount. 

Thus, if $ 100 will buy a perpetual annuity of $ 4 a year, the 
first installment being due one year hence, then $ 104 will buy 
such a perpetual annuity, the first installment being due at 
once. In the first case, the ratio of income to capital, j^^, is 
called the "rate of interest in the price sense." In the second 
case, the ratio of income to capital, y|-^, may be called "the rate 
of discount in the price sense." The rate of discoimt in the 
price sense and the rate of discount in the premium sense are 
related in a manner strictly analogous to the relation between 
the rates of interest in the two respective senses. 

As is well known, bonds, just before an installment of 
interest is due, are sold in either of two ways : they may be 
sold without the interest payment ("ex-interest"), or with the 
interest payment ("flat"). These two methods are associated 
respectively with the rate of interest and rate of discount, as 
just described. 

§ 7 (to Ch. XII, § 7) 

Mathematical Eelations between the Eates of Discount for Different 
Time Keckonings 

The rates of discount for different time reckonings are 
related in a manner quite analogous to that in which the corre- 
sponding rates of interest are related, as shown in this Appen- 
dix, § 2. Thus if V to-day will buy W in half a year, 

W~ 2' 
and if W will then buy F' in another half year on the same 
terms, 

V~ 2' 
whence, multiplying, — = 1 - — 



APPENDIX TO CHAPTER XII 367 



But yr=l-^' 

f d' 
therefore l — d={ 1 — -^ 

/d'\ 
and d = d' ' * 



27' 

from which we see that the discount rate reckoned annually 
is less than its equivalent reckoned semi-annually. Similar 
reasoning applies to quarterly and other rates. 

§ 8 (to Ch. XII, § 8) 
Dimensions of the Rates of Interest, Discount, and Capitalization 

The rate of interest in the price sense is of the form — . 

Vt 

where v represents the part of the perpetual income stream 

which flows in the time t, and V represents its capital value. 

Since, in this fraction, v and V are of the same dimension, 

both being measured in dollars, or else in bushels, or in some 

other units of same denomination, the dimensionality of the 

V 1 

fraction — reduces to - or f~\* In like manner, the ratio 
y I V 

of capitalization, being the reciprocal of this fraction, or — 

has the dimensionality t. 

These results are recognized in common usage, inasmuch as 
the rate of interest is so much per annum, and the ratio of 
capitalization is so many years' purchase. 

The same dimensionality is obtainable from the rate of 

interest considered as a premium. The rate of interest as a 

V 
premium is given by the equation — = (1 + ii) , where F' and 

V are two exchangeable sums separated by the interval t, 
usually a fraction of a year, for which the rate of interest is 
to be reckoned. Thus, if the reckoning is quarterly, t is \. 

Since V and Fare of the same dimension, — is a pure number. 

* It is interesting to observe that the dimensionality of this "price of 
capital" is entirely different from the dimensionality of the price of one 
kind of goods in terms of another, as shown in the Appendix to Chap. I. 



368 NATURE OF CAPITAL AND INCOME 

Hence its equal, 1 — ti, is a pure number. Since of this sum, 
the term 1 is a pure number, the other term, ti, is also a pure 

number. Hence i must be of a dimension reciprocal to t, i.e. -, 

or t-\ 

The rate of discount evidently has the same dimensionality 
as the rate of interest. 

APPENDIX TO CHAPTER XIII 

§ 1 (TO Ch. XIII, § 1) 

Formula for Present Value of Sum due in One Year 

If the rate of interest be denoted by i, it is evident that 1 + i 
due next year is worth $ 1 to-day, 

hence f 1 due next year is worth ■. to-day, 

and any sum V due next year is worth to-day, 

which is the general formula for the present value of a single 
sum due at the end of one year. 



§ 2 (to Ch. XIII, § 1) 

Formula for Present Value of Sum V due at End of Any Time t 

In general, it is obvious that (1+i)^ is the amount which, 
two years hence, has a present value of $ 1, hence that 

$ 1 due at the end of 2 years is worth to-day — — 

and that V due at the end of 2 years is worth to-day :. 

^ ^ {1 + if 

Similarly, V due at the end of 3 years is worth to-day — — — 

V 



and V due at the end of t years is worth to-day , ^ 

^ ^ (1 + 0' 

The last formula is perfectly general. It is not even nec- 
essary that t should be an integer. The reader who is mathe- 
matically inclined will have no difficulty in proving that the 
formula applies if the period of time is 3^ years or any other 
time whatever. 



APPENDIX TO CHAPTER XIII 369 

§ 3 (to Ch. XIII, § 3) 
Formula for the Present Value of a Perpetual Annuity 
The proposition that the present value of a perpetuity is 
- was proved in the preceding chapter. An alternative proof, 

and the one which is usually given in treatises on annui- 
ties, is as follows: Consider a perpetual annuity of $1 
per annum; it is required to find the capital value. It is 
evident from what has preceded that the first payment, 
$1, being due at the end of a year, has a discounted 

value at the present time of : ; the second has a present 

worth of — -; the third, • ; and so on indefinitely. 

(l + if (l + if ^ 

Therefore, the present value of the entire series will be, — 

rr—-- + /-, , .s2 + /I , -NO + etc., ad inf. 

If, for brevity, we substitute v for ;, this may be written, 

v + v^-{-v^ + ad. inf., 
or V (l-\-v^-\-a.d. inf.). 

Since the series evidently converges, the parenthesis is equal 

to , which may be seen by simply dividing 1 by 1 — v. 

1 — V 

Hence the value of the annuity is, v 



1-v 



which reduces to — if we substitute for v its original value. 



i ° ' 1 + i 

This sum, - dollars, is, therefore, the capital-value of an 

i 

annuity of f 1. By proportion, the capital-value of any other 
annuity a is -. 

§ 4 (to Ch. XIII, § 3) 

Formulae and Diagrams for Capital-value of Annuities payable Annually, 
Semi-annually, Quarterly, Continuously 

In case the annuity accrues semi-annually, the teeth will be 
finer, but twice as frequent. In Figure 34 we see the behavior 
2b 



370 



NATURE OF CAPITAL AND INCOME 



of the capitalized annuity if the annuity is payable annually, 
semi-annually, or quarterly. If the annuity be $4 a year, the 
teeth drop $4 if payable annually, $2, if semi-annually, and f 1, 
if quarterly. If the frequency of the installments of income be 




12 ,..-^12,^^^ 13--^'^ 
1 2 

Semi-annual Payments 



1 ' ' ' 2 

Quarterly Payments 
Fig. 34. 

indefinitely increased, we reach the limiting case of a continuous 
income, when the teeth disappear entirely and the value of the 
annuity remains at a constant level. The value of the annuity 
of $4 in all these cases, just after any installment of in- 
come is received, will be $100, if the rate of interest 
is 4%, provided the rate is respectively " reckoned annually," 
semi-annually, and quarterly in the various cases. In the 
case of continuous income, the value of the annuity of $4 
will always be $100 if the rate of interest be 4% "reckoned 
continuously." The same remarks apply, of course, to an 
annuity of any number of dollars. Its value after each install- 
ment is equal to the annual income divided by the rate of in- 
terest, or the annual income multiplied by the purchase period. 
In order to obtain the formulae for the value of a perpetuity 
payable semi-annually, quarterly, or continuously, in terms of i, 
the rate of interest reckoned annually, we need only to transform 

T,) —,i -, by means of the equations in the previous chapter. Thus 
X % o 



APPENDIX TO CHAPTEE XIII 



371 



the value of an animity of a dollars per annum payable semi- 
annually is - which, by substituting for i' its value as derived 
from the relation between i and i', viz. 1 + i = [ 1 + - ) , or 

Similarly, the 



i' = 2 ( Vl -\- i — T) becomes 
quarterly annuity becomes 



2(Vl + ^-l) 



, and the continuous 



4(^iq:^i) 

annuity, since l+i=e^ or 8=loge(l+i), becomes ^=; ^ . 

^' ^^ ^' 8 log, (1 + 

In every case the value just before an installment is found by 
adding that installment to the results just derived; and the 
value at intervening points by applying the discount curve, 
i.e. dividing the impending value (just before the next in- 
stallment) by (1 4- iy, where t is the time between the present 
and the time of the next installment. 

§ 5 (to Ch. XIII, § 3) 

Diagrams for Discontinuous and Continuous Income 

If the income installments recur annually, and are $4 each, 
these installments are represented in the line method by a, a, a, 




c c c c c c c c c c c c c 



Fig. 35. 



in Fig. 35. If they occur semi-annually, in installments of f 2 
each, they are represented by 6, b, b. If they occur quarterly, in 



372 



NATURE OF CAPITAL AND INCOME 



installments of f 1 each, they are represented by c, c, c, and so 
on indefinitely, in each case the lines becoming shorter but more 
numerous. If this process is continued indefinitely, it is clear 
that continuous income would simply be represented by an in- 
finite number of infinitesimally small lines, — a representation 
which would be unintelligible. It is for this reason that the area 
method becomes necessary. To show how it may be used, even 
for discontinuous income, let a series of annual payments, a, be 
represented in Figure 36 by the rectangles whose bases are equal 
to unity and whose altitudes, therefore, are equal to a. The point 
of time to which each rectangle is referred is taken, for conven- 
ience, as the end of each year in which it occurs. Thus the rec- 
tangle OF refers to the point of time P, and PW to Q. If the 
payments are semi-annual, we represent them by the areas of 



S T U 



O X Y Z P 



W 



Q 
Fig. 36. 



the rectangles OT, TV, etc., in the same manner. But as the 
rectangles are each equal to one half, the altitudes will no 
longer represent the individual payments, but double those semi- 
annual payments, i.e. the per annum rate. Thus, if the annu- 
ity is $4 per annum payable semi-annually, the rectangle OT 
means $2, its base is one half, and its altitude, YT, will not be 
2, but 4, the rate per annum. 

Similarly, quarterly payments are represented by rectangles 
OS, XT, TU, etc., whose altitudes will again represent the rate 
per annum of each quarterly payment. 

Finally, for continuous payments, we shall have an infinite 
number of infinitesimal rectangles, forming in the aggregate 
the whole figure represented, the altitude of which at any point 
will be the rate per annum at which income is flowing at that 
point. 



APPENDIX TO CHAPTER XIII 



373 



By limits we may pass from income which flows at a uniform 
rate to any income stream. Evidently, therefore, any con- 
tinuous income-stream may be represented by a curve (Fig. 37) 
of which the ordinate represents the per annum rate of flow at any 




point of time, and the area EC between any two ordinates BE 
and CF represents the total income which flows within the time 
intercepted between those ordinates. 

For the case of uniform flow, the continuous income stream 
is represented in Figure 38 by the area OB. OA represents the 



Fig. 38. 



rate of income, and OC represents the capital-value of this in- 
come. This capital-value remains constant, as shown by the 



374 



NATURE OP CAPITAL AND INCOME 



horizontal line CD, and the rate of interest (reckoned continu- 
ously) IS — . 

§ 6 (to Ch. XIII, § 5) 
Formula for Capital-value of a Terminable Annuity- 
Let a represent the annual payment of the annuity, t its 
duration or term, and V its present value. We are required 
to find V in terms of a, t, and i, the rate of interest. We 
have observed that a man who owns such a terminable 
annuity owns the difference between a perpetual annuity be- 
ginning at present and another perpetual annuity deferred t 
years. Consequently, the value of his property is the differ- 
ence between the values of these two ; that is, it is equal to the 
value of a perpetual annuity beginning now, less the present 
value of a perpetual annuity beginning t years hence. The 
deferred annuity which begins at the end of t years will, we 

know, be worth then the sum of -, and will be worth now what- 

i 

ever is the present value of this -. This present value is of 

i 

course found simply by discounting the ^ just obtained, and is 



(1 -L ^-y ' ^^^^ expression should therefore be subtracted from 
the value of the other perpetual annuity which begins now, of 
which the present value is ■?. This subtraction gives the 



formula, 



Hi + 0' 



§ 7 (to Ch. XIII, § 5) 

Discussion of Formulae for Terminable Annuity by Diagrams. "Total 
Discount." "Total Interest." Depreciation. 

In Figure 39 let AB represent the term t of the annuity, AD 
the value of a perpetual annuity beginning at the point of time 
A, and BE the equal value, taken at the end of the term, of a 
deferred perpetual annuity beginning at that time. Now the 



APPENDIX TO CHAPTER XIII 



375 




Fig. 39. 



present value at time A of the value BE, at time B, is evi- 
dently AC, found by drawing the discount curve CE. There- 
fore the value of the terminable annuity is equal to AD — AC, 



376 



NATURE OF CAPITAL AND INCOME 



or DC, wliicli is the total discount on BE; i.e. the amount by 
which it is, as Bohm-Bawerk says, " diminished in time per- 
spective." 

Similarly, the capital- value of the annuity, taken at any time , 
later A! (just after an installment of income), is equal to the 




smaller sum GH. Thus the capital-value gradually decreases 
in accordance with the distance of the curve CE from the 
line DE. 

In this representation the discount curve was drawn through 
E. If another is drawn through D it may be shown that EF 
is the "amount" of the terminable annuity, or its value at the 
time it terminates, if we suppose that each individual item is put 
at interest from its date to the point of time B. This "amount," 
EF, is called the " total interest " on that capital in that interval. 

In the same way, at any intermediate time just after an install- 
ment, GI will represent the value of the annuity concentrated 
at that point, and this value will consist of two parts, HG, 
which is the (discounted) value of the part subsequent to K, 
and HI, the (accumulated) value of the part preceding K. 



APPENDIX TO CHAPTER XIH 



377 



The decrease in capital-value of the annuity, which has been 
represented by the approach of CE to the horizontal line DE 
above it, is better represented, however, by inverting CE to 
the position KB, in order that the capital-value may be repre- 
sented, as in our previous examples, by the distance from the 




Fig. 41. 



horizontal line AB below it. This change is accomplished 
in Figure 40. The value of the annuity taken after each 
installment of income is represented by the ordinate, as mA\ 
of the curve KB, and the value just before an installment 
is represented by the ordinate, as nA^', of a point above this 
curve a distance equal to that installment. The value at inter- 
mediate points evidently follows a discount curve, as mn, be- 
tween these two points. The result is that the capital-value 
will rise and fall according to the steps, or teeth, shown in the 
diagram. 

As the income items become more numerous the teeth be- 
come more frequent and smaller, and disappear when the flow 
of income is continuous, as represented in Figure 41, where the 



378 NATURE OF CAPITAL AND INCOME 

curve KB itself represents the capital-value at all points of 
time. 

The formula for the present value (F) of the annuity just 
after each installment of income is the same, whatever the 
time intervals between installments. This is strictly true, how- 
ever, only on the proviso that the rate of interest i is to be 
understood as reckoned in accordance with the frequency of 
the installments of income in each case, — semi-annually, quar- 
terly, etc., — instead of annually, as has been hitherto under- 
stood. 

The formula for the capital-value, V, just before an install- 
ment is evidently found by taking the preceding formula for 
Fand adding a. This gives, — 

a 

/-# ■3* 



^ {1+iy 

At intermediate points the capital-value is equal to the 
amount just named discounted for the interval elapsed be- 
tween the point of time considered and the next installment 
of income. 

§ 8 (to Ch. XIII, § 7) 
Formulge for Value of a Bond 

To be general, let us suppose a bond, the income from which 
is a dollars per year, payable annually for t years, at the end of 
which time, in addition to the final payment a, another larger 
payment P, called " principal, " is paid. We are required to 
find the present value, V, of these future expected payments 
for a given rate of interest, i. 

The discounted value of the terminable annuity has already 
been expressed, namely, — 



i {1 + iy 
The discounted value of P deferred t years has also been 
explained and is evidently, — 

P 

(1 + 0'* 



APPENDIX TO CHAPTER XIII 379 

The sum of these expressions is the value V, "which we are 
seeking. In other words, — 

a 

F=^ L— + "^ 



i (1 + 0* (1 + 0' 



or t;-_ a * 



i (1 + 0' 

Some special cases may be considered. First, if the annual 
income a is the interest on the " principal " P, — i.e. if a = Pi 

[ orP = ^|, — the second term vanishes, as its numerator is 



a 



evidently zero, and since the first term, -, is by present hy- 
pothesis P, the equation then becomes V=P. 

Secondly, if a is greater than iP, it may be readily shown that 
V will be greater than P ; and if a is less than iP, that V is 
less than P. 

The formula given is of practical importance, as it enables 
us to compute the price at which a bond must sell in order to 
yield a certain rate of interest. 

To apply the formula numerically we need only to assign 
particular values for the magnitudes involved. Let us take the 
numerical case already considered, where P=$100, a = $5, 
i = .04, and t = 10. In this case the formula becomes, — 

.04"*" (1.04)i« ' 
which reduces to 108, as we found before. 

Similarly, it may be shown that if bonds are sold on a 6 % 
basis, the price of the bond in question would be $ 921 

We have derived the value of a bond, V, just after a 
payment of "interest." In this case the bond is said by 
brokers to be sold " ex-interest." If, on the contrary, it is 
sold " flat," that is, with interest, its value will evidently be 
increased by the " interest " a, and will be 7"+ a. The price 

at any time between installments will evidently be ,^ ^ ,, 

^ ^ (1+0 



380 NATUKE OF CAPITAL AND INCOME 

where V represents the value the bond will have after the next 
"interest" payment, and t' the time elapsing to that payment. 
Or, it is F(l + t)' ", where F represents the value after the 
last "interest" payment, and t" the time since said payment. 
Practically this last formula reduces to F+ Vit", which in turn 
is practically the same as V+ at" ; for a and Vi are practically 
equal, each being nearly the true interest for one installment 
period. This is the formula usually employed by brokers, at" 
being called the " interest earned " since the last coupon. 

§ 9 (to Ch. XIII, § 7) 

Alternative Method, whereby the "Premium" in the Price of the Bond 
is compounded separately 

The so-called 5 % bond running for 10 years, which is sold 
on a basis of 4 %, may be considered as consisting of the follow- 
ing two property rights : (1) the right to four dollars a year 
for 10 years and f 100 at maturity, and (2) the right to one 
dollar a year for 10 years. It is evident that the present 
value of the first property is $ 100, to which, therefore, we need 
only to add the value of the second property, namely, the an- 
nuity of f 1 a year for 10 years. It is therefore the present 
value of this small annuity, consisting, we may say, of the 
difference between the real and nominal interest on $100, 
which constitutes the "premium" on the price of the bond. 
This present value is f 8, and is found in the manner already 
explained for terminable annuities, being the total discount on 
$ 25 at the end of 10 years, f 25 being the capital-value of a 
perpetual annuity of f 1 a year, when interest is reckoned at 
4%. Consequently, the bond is worth in all f 108. This value 
is represented diagrammatically in Figure 42. 

Let A A' represent the 10-year period, with the f 5 interest 
payments shown by the ten vertical lines at unit intervals. 
A'B' represents the $100 "principal" due in 10 years, and 
AB represents what the bond would be worth ($100) if the 
interest payments were $4 instead of $5. To this must 
therefore be added the present value of $ 1 a year for 10 years. 
This is the total discount on B'C (drawn equal to $25), the 
capitalization of a perpetual annuity of $ 1 a year. The total 



APPENDIX TO CHAPTER XIII 



381 



discount on this $25 is shown by the line BD, which is there- 
fore the premium in the selling price of the bond. The total 
price is AB-\-BD = AD. The price at later dates (taken 
each just before an installment) is represented by points on 




Fig. 42. 



the discount curve D5' drawn with reference to CC as a 
horizontal axis. Adding at each of these installment points a 
line equal to $5, we have the value just before interest pay- 
ments, and connecting the tops of these lines with the preceding 
interest intervals by discount curves reckoned at 4%, we have 
a series of teeth representing the normal course of the price of 
the bond from the present to maturity. 

In case a bond is sold at a 6% basis, we have the curve B'D', 
instead of B' D, with the teeth superimposed as before, the 
tooth curves, however, being in this case on a 6% slope. 



382 NATUEE OF CAPITAL AND INCOME 

§ 10 (to Ch. XIII, § 7) 

Formula for a Bond, when Interest is reckoned oftener than yearly 

The formula in the case of semi-annual income when in- 
terest is reckoned semi-annually is evidently, — 

which applies just after an interest payment ; just before, it 
is evidently F+-; and at intervening intervals it is this value 

discounted, or for practical purposes, the simple formula, 
y-\-at\ where V is the value taken after the last "interest" 
payment, and t the time elapsing since that date. For the case 
of continuous interest, if we let, as in the previous chapter, 
8 represent continuous interest, we have, — 



p_a 



F=?+- 



which formula remains unchanged during the entire period of 
the bond. 

These various formulae may, of course, be somewhat trans- 
formed and simplified for practical purposes. Moreover, they 
may all be transformed in terms of the various rates of 
interest. Some actuaries apparently prefer to use, as the in- 
terest rate, only the "effective" rate, i, which is what we call 
the "rate of interest reckoned annually." The preceding 
formulae, which employ the semi-annual, quarterly, and other 
forms of interest rates, may be transformed by substituting 
their values in terms of i, in accordance with the relations 
shown in Appendix to Chap. XII, § 2. 

§ 11 (to Ch. XIII, § 8) 

Formula for Capital-value of Any Series of Income Installments 

We may express, in general formulae, the capital-value of 
any income stream, as follows : Let %, a^, Og, represent the 
successive installments of income accruing at various times dis- 



APPENDIX TO CHAPTER XIII 383 

tant from the present instant by the intervals ^i, U, t^, etc., which 
may be equal or unequal, whole or fractional, or even positive 
or negative according as the income is in the future or in the 
past. Let i represent the rate of interest. The present value 
of such an income stream will be, — 

F= — ^ 1 ^ \ ^ h , etc. 

(1 + t)'i ( 1 + iy^ (1 + iy 

Or, in briefer notation, 

V=V ^ 

^(1 + i)'' 
where % is taken in its usual sense of the summation of the 

series of terms of the type of that following it. 

§ 12 (to Ch. XIII, § 8) 

Diagram and Formula for deriving Capital-value from a given Continuous 
Income Stream 

For any income stream flowing continuously, and represented 
in Figure 43 by the area below JO/, the capital- value will 
be represented by the curve NO. The ordinate of the income 
stream at any point, as US, represents the rate of its flow at that 
point, and any area, as IiSS"Ii", represents its total flow through 
the period RR". The ordinates of the curve NO will repre- 
sent the capital-value of this income stream. NO is con- 
structed from N backward as follows : the curve begins at N 
on the income stream and is generated by a point moving in 
such a manner that at any position its direction of motion 
is the resultant of two tendencies. To represent these 
two tendencies we draw through the discount curve OP. 
Tangent to this curve we draw OH so as to meet the line QH 
drawn vertically and distant to the left one unit from OK. 
OH represents one of the two tendencies mentioned, that due 
to discounting the future. OK drawn vertically up from 
and equal to MS, the rate of income at that time, represents 
the other tendency. The resultant, OQ, drawn according to 
the principle of the parallelogram of forces, will represent the 
actual direction in which the curve will be moving at the 
point 0. In other words, a point moving under the influ- 
ence of two forces, OK and OH, will generate the required 
curve NO. 



384 



NATURE OF CAPITAL AND INCOME 



In order to show that this is a correct representation let us 
first take the case of semi-annual income. RR" represents one 
year ; Rr represents half a year. Draw the ordinate rh. From 
h draw vertically upward hq to represent a half-year's install- 
ment of income, that is, half of Rs. To avoid complicating the 
figure, hq is omitted; were it drawn, q would lie on the line OQ'. 
Then, according to our previous representation, the capital- 
value will follow the curve Ohq, which forms a "tooth." The 
line Oq is therefore a line drawn through the top points of two 
neighboring teeth. Its direction is a first approximation to 




Fig. 43. 



the direction OQ of the curve for the continuous case. This 
direction Oq is the diagonal of a parallelogram formed by 
producing Oh to meet the ordinate from W in H', producing 
Oq to Q' and completing the parallelogram. 

Since H'Q' is twice as far from as hq {i.e. RR" =2 {rR) 
by hypothesis), it follows, by similar triangles (i.e. Ohq and 
OH'Q'), that it is also twice as long. But hq represents a 
half year's installment of income. Hence H'Q' represents two 



APPENDIX TO CHAPTER XIII 



385 



such installments, or the annual rate of income. Therefore 
OK, being of the same length, also represents this annual rate 
of income. 

In other words, the direction from to g lies along a paral- 
lelogram of which the side OK represents the annual rate 
of income and the side OH' a chord of the discount curve 
OP. 

Now it is evident that if, instead of a semi-annual installment, 
we assume greater frequency, the same statement will apply 
except that the point h will be nearer 0. By proceeding in this 




Fig. 44. 



manner the chord OliIF approaches the tangent OH as its 
limit, and the parallelogram OH'Q'K becomes at the limit 
the parallelogram OHQK as originally described. That is, its 
sides are OK, the annual rate of income, and OH, the tangent 
to the discount curve drawn from to a vertical line one year 
to the left. 

That this construction and its demonstration bear a striking 
analogy to the construction and demonstration which apply to 
2c 



386 



NATURE OF CAPITAL AND INCOME 



the composition of forces or motions is very evident. Availing 
ourselves of this analogy, we may say that in the case of dis- 
continuous income, the point traces the capital curve (back- 
ward) by obeying alternately two tendencies, — one, to follow 
the discount curve at times when no income occurs, and the 
other, to rise vertically whenever income occurs. In the case 
of continuous income these motions occur simultaneously 
instead of alternately, and the resultant is a smooth curve 
instead of a series of teeth. 

The same principles apply when part of the income curve 
is below the horizontal axis, representing negative income. If 




Fig. 45. 



at the beginning the prospective cost just counterbalances the 
prospective income, the capital-value will at that instant be 
zero, and will from that point rise and fall again to zero at the 
end, as indicated in Figure 44. 

The formula for capital-value in the case of a continuous 
income stream will be, — 

1^_ r da 

^~J (1 + 0" 

in which da may be said to represent the infinitesimal income 
which flows in the infinitesimal increment of time dt. In other 
words, da represents an infinitesimal element of the area ABC 
(Fig. 45), of which element the base or breadth represents the in- 
finitesimal time dt. For the purpose of integration we may sub- 
stitute for da the expression /(i)d«, where /(i) represents CB, or 
the ordinate of the income stream taken as a function of time t. 
If the special form of the function / (t) is known, it is evidently 
possible to integrate the expression and obtain its value for any 
given limits. 



APPENDIX TO CHAPTER XIII 



387 



§ 13 (to Ch. XIII, § 8) 

Diagram sho-wingthe Accumulated "Amount" of a Given Income Stream 

We reproduce in Figure 46 the diagram with which we began 
the study of the general case of capitalizing income. We now 
wish to obtain the accumulated value A"'Q, at the close of the 
period OA'", of the income items AB, A'B', A"B", and A"'B"'. 




This consists of : (1) A"'B"' itself ; (2) B"'£!, which is the amount 
of CD" (or its equal, A"B"), and is found by continuing the 
discount curve CD" to E; (3) EF, which in like manner is the 
amount of CD' (or its equal A'B') ; and (4) FQ, which is the 
amount of CD (or its equal AB). Thus, while OP represents 



388 NATURE OF CAPITAL AND INCOME 

the price of the stream if paid for in advance, A"'Q repre- 
sents the price if paid for at the end. By similar reasoning 
it may be shown that the price at any intermediate point of 
the entire series is the height of any point on the one smooth 
curve PQ. 

This result must not be confused with that which represents 
the capital-value of future income. Thus, at the point of time 
0', the line O'P represents the value of all the income items, 
past as well as future, AB, A'B', A"B", A"'B"', whereas the 
line O'P" represents the value of only the future items A"B" 
and A"'B"'. 

§ 14 (to Ch. XIII, § 10) 

Effect of reckoning Semi-annually, Quarterly, and Continuously, on the 
Eate of Interest realized on a Stock or Store of Articles 

As usual, the passage from the rate of interest reckoned 
annually to the rate of interest reckoned continuously, if accu- 
rately considered, is not so simple as appears on the surface 
and may afford to some readers no little perplexity. If we 
assume, for convenience, that each article in the merchant's 
stock remains there for a definite period, called the time of 
"turn-over," and the cost of purchase and all the other costs 
connected with the article occur at the time it enters the 
stock, while all the receipts or gross income from that article 
occur at the time that it leaves the stock, we may pass from 
the case of the rate of interest "reckoned annually" to that 
of the rate of interest " reckoned continuously " as follows : — 

As a first step we assume that all of the stock is bought at 
the beginning of a calendar year and sold at the end, so that 
the time of turn-over is one year. If the cost of the stock is 
represented by c, including not only the purchase price but all 
other elements of cost, this must represent the discounted 
value of the receipts at the end of the year, which are there- 
fore c(l + i). The net income for the year is, therefore, 
c(l + i)--c, or ci. This bears a ratio to the total cost value 
reckoned at the beginning of the year, namely c, of — , equal 
to the rate of interest, i. 

For the second step we consider the stock as half purchased 



APPENDIX TO CHAPTER XIII 389 

on January 1 and half on July 1, six mouths later, and that, 
as before, each element of the stock remains one year before 

sale. The cost on January 1 is -, and on July 1 is also -. 
If we take inventory on July 1, the stock just purchased rep- 
resents a value -, while that purchased six months before, and 
which is to be disposed of in six months more, may be taken 
as having a somewhat greater value, namely, ^VT+T the 

latter being the cost value plus interest, or, what amounts to 
the same thing, the expected selling value less interest. The 
total stock is therefore worth on July 1, — 



2 + 2Vl + i. 
The sales or receipts from the stock will evidently be every six 
months - (l-f-*)> ^^^^ being the accumulated value for one 

year of the amount purchased, ^. For the entire year the 

receipts will thus be just double, or c (1 -|- 1). If from this 
we deduct the per annum cost, c, we obtain, as before, the 
net income, ci The ratio of this net income to the capital- 
value taken on January 1 or July 1, of any year, will therefore 
be, — 

ci 



2+2^1+* 

This expression, which is evidently the same as , 

1+ VI + t 
seems no longer to be equal to the rate of interest ; but the dis- 
crepancy is due to the fact that the merchant's income accrues 
semi-annually, whereas i is reckoned annually. If we substi- 
tute for i its value in terms of i ', the rate of interest reckoned 

semi-annually (namely, i' + j , as shown in the Appendix to 

Chap. XII, § 2), we shall find, on simplifying, that the above 
expression reduces to i'. In other words, in the artificially 
simple case in which the merchant is supposed to accomplish 



390 NATURE OF CAPITAL AND INCOME 

all his buying and selling in two equal amounts and at semi- 
annual intervals, the ratio of his annual income to his capital, 
reckoned at these times, is i '. In the same manner it may be 
shown that if his buying and selling take place at quarterly 
intervals, the ratio of his income to his capital reckoned at these 
times will be V, i.e. the rate of interest per annum reckoned 
quarterly ; and so on indefinitely until we reach the limiting 
case, approximately true in practice, in which the merchant buys 
and sells daily, when we find that the annual net income, 
divided by the value of the capital at any instant, is equal 
to the rate of interest reckoned continuously. It will be observed 
that to make this proposition hold good it is necessary 
that the valuation of the merchant's capital shall be, not 
its wholesale price nor its retail price, but something inter- 
mediate, which shall take account of the fact that the stock 
cannot all be sold immediately, and that, on the other hand, it 
will not be necessary to wait a year before it is all sold. Similar 
reasoning may evidently be applied in case the time of turn- 
over of the stock is more or less than a year. 



§ 15 (to Ch. XIII, § 11) 

Influence of Variability of Eate of Interest 

Thus far we have treated the rate of interest in successive 
years as invariable. As a matter of fact, the rate of interest 
is constantly fluctuating. We shall suppose at first that these 
fluctuations are foreknown, and for convenience we shall confine 
ourselves to a year as the standard interval of time. Let us 
assume that the rate of interest for the first year is ^l, for the 
second year, i^, for the third year, 4, and so on indefinitely, all 
of these being supposed to be known in advance. By means of 
these rates of interest we can calculate the present value of 
any item or series of items of income. Thus, if ^ 1000 is due 
in two years and the rate of interest for the first year (ij) is 
5%, while the rate for the second year (is) is 3%, we can 
obtain the present value of the f 1000 by discounting it at 3 % 

for one year, thus obtaining -zr-ir^, or $970.87, as its value a 



APPENDIX TO CHAPTER XIII 



391 



year previous to the due date, or one year from the present, 
and rediscounting this 970.87 at 5% for one year, giving 

' , or $924.30, as the present value. 
1.05 

In general, if V represents the item of income to be received, 
its value in one year will be and its present value, 

1 + *2 

V 



(1 + i,) (1 + 4)' 
w^hich formula is, of course, easily extensible to three or any 
number of years. 

If we represent the future value V in Figure 47 by the line 
-AB, its value in one year is CF, found by the 3% discount 



Fig. 47. 



curve BC, and its present value is ED, found by the 5% dis- 
count curve DC. In other words, instead of having a uniform 
discount curve from B to D, we have a broken discount curve 
BCD, with a different percentage rate of rise for the two 
years considered. 

In this way we may obtain the present value of any series of 
income items precisely as before, with the exception that the dis- 
count curves are now somewhat irregular. Thus, if the series 
of income items at different points of time are of the magnitude 



392 



NATURE OF CAPITAL AND INCOME 



represented in Figure 48 by AB, CD, EF, and GH (read in tlie 
order of futurity), the remotest item, AB, is discounted by 
means of the discount curve BC, and the next to the last item 
is added to the capital-value at C, bringing the capital-value to 
the point D, from which the next discount curve DE is drawn, 
and so on until we reach the point /. Z7is thus the capital- 
value of the given series of income items. 

In this way it is possible to review all the special cases 
of capitalizing income which were considered in Chapter XIII, 




Fig. 48. 



and correct them for the general case of a rate of interest 
which is variable but foreknown. Such a calculation, how- 
ever, is of very little practical consequence, inasmuch as the 
variations in the rate of interest are seldom if ever foreknown. 
Were it worth while to pursue the subject, it would 
be convenient to simplify the calculations by substituting, 
where possible, for the series of rates of interest i-^, ij, 
?3, etc., an average, ,/, such that if the given series of in- 
come items were discounted uniformly according to the rate 
of interest j, we should obtain exactly the same present 
value as when the several separate rates ij, i^, h, etc., are 
employed. The formula for the average rate of interest j of 



APPENDIX TO CHAPTER XIII 393 

any particular number of individual rates, as i^, i^, is, etc., 
used for discounting individual items of income, ai, ttg, ag, 
would evidently be, 

"^ + ^^ + ^^ +...= 



1+i (i+jy (i+jY 



+ .....:!... + ... ■..."^... . .. +. 



Various applications of such formulae might be made, though 
they have little practical utility. Thus, the value of a termi- 
nable annuity of a given term is found, as before, by taking the 
difference in value between a perpetual annuity beginning to- 
day and a perpetual annuity deferred to the end of the given 
term. The value of the perpetual annuity beginning to-day 
would be found, as has just been shown, by dividing the annual 
income a by ji, the average rate of interest of the individual 
rates from the present into the indefinite future. The value 
of the deferred annuity taken at the end of the term would be, 

in like manner, — , where jt is the average of the individual 

Jt 
rates from that point indefinitely forward. The present value 
of this deferred annuity would be found by discounting the 
latter value for the term of the annuity according to the rate 
ji^t where j^^t is the average of the individual rates of interest 
h) hf hi • • ' % for the term of the annuity. 

The value of a bond would be found in a similar manner. 
We have just shown how to find the present value of the 
"interest" of the bond, and the present value of the "princi- 

p 
pal," P, due at maturity, would be evidently — ^ — ^ . 

§ 16 (to Ch. XIII, § 11) 

Representation of Capital and Income by Polar Coordinates 

The mathematical reader may be interested in an alternative 
method of representing income and capital, by which polar 
coordinates are employed instead of rectangular. Let the 
radius vector in Figure 49 represent the parent capital. The time 
required for a complete revolution of the radius vector may be 



394 



NATURE OF CAPITAL AND INCOME 



taken to represent the " purchase period. " Thus, if the rate of 
interest is 4 %, the purchase period is twenty-five years. During 
one year the radius vector will move through an angle ^ of a 




Fig. 49. 



complete revolution, and the length of the radius vector will 
increase from OA to OB by an amount, BC, -^-^ of the original 
OA, interest being 4 % reckoned annually. In case the inter- 
est BC is not reinvested, but detached from the principal, next 



APPENDIX TO CHAPTER XIII 395 

year will bring the radius vector to the position OD, at which 
time the same interest, DE, may be detached, and so on in- 
definitely, the result being a toothed wheel. Each tooth being 
^ig- of the radius OA, the sum of the twenty-five teeth will be 
exactly equal to the radius. In case the interest is reckoned 
semi-annually, the teeth will be fifty in number instead 
of twenty-five, but each will be half as large; and so on 
until, for "continuous" reckoning, we have an infinite number 
of teeth each of infinitesimal size; but the sum of the whole 
number in the complete revolution will still be exactly equal 
to OA. 

In case no income is received, the accumulation of capital is 
represented by increasing the length of the radius vector, the 
end of which thus traces a spiral. The radius vector re- 
volves around the spiral once every twenty-five years, 
and the ratio between the "amount," OA', after a com- 
plete revolution, and the original "principal" OA, will be 
e, that is, 2.718, provided the rate of interest is reckoned 
continuously. 

The same spiral represents the accumulation of capital, 
whatever may be the rate of interest. For a complete revolution 
does not represent a definite length of time, but the purchase 
period ; and it is clear that a more rapid rate of interest is repre- 
sented by a more rapid turning of the radius vector. Thus, if 
the rate is not 4%, but 8%, the radius vector swings around 
through the same spiral once in twelve and a half years instead 
of once in twenty-five years. Again, if the rate is 2%, the 
revolution is fifty years. The spiral is what is known as the 
"equiangular spiral," and has the property that the tangent at 
any point is inclined at a constant angle to the radius vector. 
The angle is in this case such that its tangent is 27r. This 

angle is 80° 57'. The equation of this spiral is — = e"'^, in 

which p represents the radius vector, 6 the angle of revolution, 
and po the initial radius vector; e and tt are, of course, the 
magnitudes ordinarily represented by these letters, namely, the 
base of the Napierian system of logarithms and the ratio of 
the circumference of a circle to its diameter. 



396 NATURE OF CAPITAL AND INCOME 

APPENDIX TO CHAPTER XIV 

§ 1 (to Ch. XIV, § 5) 

When the Interest Eate varies, there are Two Rival Concepts of Standard 

Income. 

When the rate of interest varies during successive years, the 
standard of the comparison of income and capital requires re- 
statement. We found, vrhen the rate of interest was assumed 
constant, that the standard income corresponding to a given 
capital was a perpetual and uniform flow, of which flow that 
capital was at any time the present value. It did not matter 
whether standard income was conceived as income which 
was constant and perpetual, or as income which would main- 
tain its capital-value at a constant level ; for under the con- 
dition of a constant rate of interest, a constant income will 
necessarily maintain a constant capital-value. But when we 
introduce the possibility of a change in the rate of interest, 
these two concepts of standard income are no longer equiva- 
lent; under such conditions only an inconstant income will 
maintain a constant capital-value. Thus, if the rate of interest 
for the first year is 10%, for the second, 5%, and for the third, 
6%, etc., the income stream which will maintain the capital 
unimpaired will be, in successive years, proportional to the 
numbers 10, 5, 6, etc. A person possessed of $100 of capital 
can evidently earn with it $10 the first year and still have his 
$100 unimpaired, with which, in turn, he can earn $5 the 
second year and maintain the principal of $100 ; and again 
$6 in the third year, and so on, receiving each year an income 
proportional to the rate of interest. Relatively to this income 
stream considered as a standard of reference, the propositions 
stated in Chapter XIII will remain true, namely, that if the 
real income in any year exceeds the standard for that year, the 
capital will be impaired by the excess ; and if the income falls 
short of the standard in any year, the capital will accumulate 
by the amount of the deficiency. 

But this concept of standard income is not the only legiti- 
mate one. We may, if we choose, employ the other definition 
of standard income, as a perpetual and uniform flow. In this 



APPENDIX TO CHAPTER XIV 397 

case, it is the capital-value of such an income stream which 
will vary from time to time. As has been seen, the capital- 
value of such an income stream is found by dividing the rate of 
income a by the average of the individual rates of interest, such 
as, in the above example, 10%, 5%, 6%, etc., ad inf., the aver- 
age being obtained by the formula given in Appendix to Chap. 
XII, § 5. If such average rate of interest be called ji, the 

capital -value will be -. Suppose, for instance, that the person 

has a uniform perpetual income of $5 per annum. If the rate 
of interest to-day, ji, is 5%, the capital-value to-day will be f 100. 
If next year, Jg (the average of the future rates in individual 
years, beginning at that time) is 4.9%, the capital- value will 
be f 102. If, two years from date, js be 5.1%, the capital-value 
will sink to $98. Adopting such an income stream as a stand- 
ard, the propositions as to impairment or increase will still be 
true, provided such impairment or increase is measured with 
reference to the variable capital-value just shown. Thus, if at 
the end of the first year more income than $5 is received, the 
capital-value will be impaired by the difference, this impair- 
ment to be reckoned with respect, not to f 100, but to $102, 
which would be the value had the income remained standard. 
Thus, the effect of a difference between real and stand- 
ard income may be stated in the same terms, whichever of the 
two definitions of standard income is adopted. In the one case 
the standard is with reference to constant capital and variable 
income ; in the other, to variable capital and constant income. 
In practical life, the former standard is usually employed, 
although for certain purposes the latter would be more suitable. 
We all know of cases of investors who, twenty years ago, in- 
vested at a high rate of interest, and who have taken pains 
merely to maintain the value of their capital unimpaired, 
although they were well aware that the rate of interest was 
constantly sinking. In consequence, these persons are now 
forced, when reinvesting, to suffer a large decrease in income, 
which could have been avoided had they kept in view the main- 
tenance, not of their capital, but of their income, and laid aside 
each year a certain sum in order to offset the fall in the rate of 
interest. The reason such a procedure is not common is 



398 NATURE OF CAPITAL AND INCOME 

that the fall or other change in the rate of interest can never 
be foreseen with precision, and thus a perfectly uniform flow of 
income secured, whereas it is always possible, in the case of 
safe investments, to calculate what is necessary to maintain 
the value of the capital at a uniform level. 

§ 2 (to Ch. XIV, § 12) 

Effect of Foreknown Tax on Increase of Capital 

Let us suppose that the three brothers invest in their respec- 
tive annuities without realizing that a tax is to be imposed. 
The first brother has bought with his $10,000 a perpetual annu- 
ity of $500 a year; the second, a perpetual annuity of $1000 
deferred 15 years ; and the third, an annuity of $2000 for six 
years only. After these investments have been made, let us 
suppose that the tax of 10% on income is announced. If "in- 
come" is interpreted properly, i.e. as simply the annuities, 
the value of each of the three properties will immediately 
shrink by $1000, so that any of the three brothers could sell 
his annuity, subject to the tax, for $9000. But if the "income 
tax" is interpreted as a tax on "earnings," i.e. on income and 
increase of capital, the announcement of such a tax will not only 
reduce the values of the three properties very unequally, as has 
been shown, but will have the further effect of altering the very 
annual increase in the value of the capital which is subject to 
taxation. To show the effect of this " repercussion," let c rep- 
resent the value of the capital of the second brother (who saves) 
at the end of any year during which no (true) income is received. 
Thus c is $18,000 at the end of the fifteenth year when the an- 
nuity of $1000 a year is purchased ; for the capitalization of 
the perpetuity of $1000 which begins at that time is $20,000, 
from which $2000 is deducted as the capitalized tax. Let i 
represent the rate of interest (as 5%) and t the tax rate (as 
10%). We wish first to find x, the capital-value one year 
earlier than c. It is clear that x is the discounted value 

of c [i.e. — — ] less the discounted value of the tax, which 

V 1 + V 
we will suppose is due at the end of the year. The tax 
is laid on the increase of capital-value in the year, i.e. on 



APPENDIX TO CHAPTER XIV 



399 



c — x. As the rate is t, the tax is (c — x)t. The discounted value 



of this tax is 

c 



(c — x)t 
1 + i' 



This deducted from the discounted 



vahie, ^ "^ . , of next year's capital-value is this year's capital- 

c (c — x)t 



1 + i 
value, X ; i.e., — 



Solving for x, we have, x- 



1+i 1 + i 

1 — t + i 
The tax itself is t(c — x), which, if we substitiite for x its value 

just found, reduces to . 

1 — t + i 

If we substitute for i and t their assumed values, .05 and .10, 
we have x = c x .947 

and tax = c x .0053. 

Substituting for c its value at the end of the fifteenth year, 
namely, $18,000, we find that x, the value one year earlier, 
will be 18,000 x .957, or f 17,046, and that the value one year 
previous will be the latter sum multiplied likewise by .947, or 
$16,142.56, and so on until the present is reached, when the 
value will be $7,952.15. The table below will show, there- 
fore, the total effect of a 10% tax on the increase of value, 





Capital-value 


Increase op Capital- 
value 


10% Tax Thereon 


Beginning- 


$ 7,952.15 






End of 1 year 


8,397.20 


$445.05 


$44.51 


End of 2 years 


8,867.27 


470.07 


47.01 


End of 3 years 


9,363.54 


496.27 


49.63 


End of 4 years 


9,887.58 


524.04 


52.40 


End of 5 years 


10,440.95 


553.37 


55. .34 


End of 6 years 


11,025.29 


584.34 


58.43 


End of 7 years 


11,642..33 


617.04 


61.70 


End of 8 years 


12,293.91 


651.58 


65.16 


End of 9 years 


12,982.06 


688.15 


68.82 


End of 10 years 


13,708.62 


726.56 


72.66 


End of 11 years 


14,475.84 


767.22 


76.72 


End of 12 years 


15,286.00 


810.16 


81.02 


End of 13 years 


16,142.56 


856.56 


85.66 


End of 14 years 


17,046.00 


903.44 


90.. 34 


End of 15 years 


18,000.00 


954.00 


95.40 



400 NATURE OF CAPITAL AND INCOME 

including ttie " repercussion " of the tax on the capital-values 
themselves. 

The taxes in the table evidently differ somewhat from the 
taxes given in the text, which do not include the effect of 
"repercussion." The present value, therefore, of this tax on 
the increase of capital should be altered from $714 to $661.81. 
A similar correction should be made for the case of the spend- 
thrift. Our main object, however, is not to study the effects 
of different methods of levying taxes, but merely to show how 
untenable is the theory which includes savings under income, 
and excludes that part of true income or services which brings 
about a depreciation of capital. 

§ 3 (to Ch. XIV, § 13) 
Unrestricted Application of a True Income Tax Impracticable 

Theoretically, an income tax should tax every element of 
income, large or small, positive or negative. That is, all posi- 
tive items should have a tax and all negative items a bounty. 
This system would be ideal in theory but difficult to carry out 
in practice. 

No attempt is made in this book to contrive a practical 
system of taxation which would avoid all the difficulties which 
have been pointed out as belonging to systems now in use. It 
is undoubtedly true that it would be impracticable to assess 
taxes on each article on the basis of the actual items of in- 
come it yields ; for most of such items are simply the positive 
sides of " interactions" and are offset as outgoes in the accounts 
of some other article of capital. To carry out such a system in 
detail would require that we levy taxes on the proceeds of every 
sale and remit them on every investment. It would be difficult 
to avoid injustice, evasion, and fraud if the attempt were made 
to assess taxes on such income and remit, as would be required 
logically, taxes on the corresponding outgo. The taxpayer would 
contrive to exaggerate his outgo and understate his income. 
Consequently, the sj^stem is not wholly unjust which ex- 
empts from taxation that part of income which stands 
for impairment of capital, and assesses taxes on that part 
which swells capital, or savings. The system would be 



APPENDIX TO CHAPTER XIV 



401 



entirely just if the impairment of one capital were always 
offset by the equal increase of some other capital, i.e. if 
the taxpayer's total capital-value were kept at the same level. 
In general, large receipts are usually reinvested and should 
therefore not be subject to the income tax at all. If we could 
assume such reinvestment to be the invariable rule, we could 
approve of the system by which, in England, a terminable an- 
nuity is not taxed as income at its full value, but is taxed only 
on that part of it which constitutes "interest." The other part, 
which constitutes impairment of principal, is not taxed. The 
system, of course, fails of justice in cases where this impairment 
of principal is never restored in some other form of investment 
but ultimately represents, like the other part of the annuity, 
through personal expenditure, final enjoyable income. 

To illustrate the English exemption of impairment of capital, 
if $1000 is paid for a five-year annuity on a basis of 4 % inter- 
est (reckoned semi-annually), it will purchase an annuity of 
$111.33 at the end of each six months, and the following will 
be the schedule showing the capital-value at each interval, the 
interest accruing upon it, the payment to the beneficiary, and 
the impairment of capital resulting.^ 





Capital 


Interest 


Total 


Impair- 


Capital 




AT Begin- 


Accrued 


Payments 


ment OP 


Left at 




ning 


at End 


AT End 


Capital 


End 


1st half year .... 


$1000.00 


$20.00 


$111.33 


$91.33 


$908.67 


2d. half year . 








908.67 


18.17 


111.33 


93.15 


815.52 


3d half year . 








815.52 


16.31 


111.33 


95.02 


720.50 


4th half year . 








720.50 


14.41 


111.33 


96.92 


623.59 


5th half year . 








623.59 


12.47 


111.33 


98.86 


524.73 


6th half year . 








524.73 


10.50 


111.33 


100.83 


423.90 


7th half year . 








423.90 


8.48 


111.33 


102.85 


321.05 


8th half year . 








321.05 


6.42 


111.33 


104.91 


216.15 


9th half year . 








216.15 


4.32 


111.33 


107.00 


109.14 


10th half year . 








109.14 


2.18 


111.33 


109.14 


000.00 










$1000.00 





If at the start he has a capital of f 1000, at the end of the 

1 rrom Institute of Actuaries' Text-book, Yart I, "Interest," by Ralph 
Todhunter, p. 57. London (Layton), 1901. 
2d 



402 NATURE OF CAPITAL AND INCOME 

first half year, there is left f 908. 67, which has impaired 
his capital by f 91.33. This being reinvested and yielding in- 
terest, would make a total combined fund of $1000 as before. 
At the end of the second half year, in like manner, the original 
security is worth $815.52, but to this must be added the 
capital invested last year, $91.33, and also the investment this 
year, $93.15, making a total again of $1000; and so on for 
each year. 

If, then, as in England, the tax is paid on the interest 
annually (second column), no injustice is done, providing the 
items in the fourth column are actually reinvested each year, and 
that the interest on such reinvestment in some other form is 
used as income. In other words, each reinvestment is not ac- 
cumulated at compound interest, but made a separate fund 
yielding perpetual interest which is converted into enjoyable 
income as fast as it is received. In this case the man will be re- 
ceiving, from the given security and the others created out of 
his reinvestments, a uniform net income of $20 a year, and 
will maintain his capital at $1000. Consequently the ex- 
emption of "impairment of capital" works no ultimate injustice, 
since ultimately there is no such impairment. 

But as, practically, we can never know to what extent the 
" impairments " are actually reinvested, the justification of tax- 
ing the sums in the first column instead of those in the third 
is entirely on grounds of expediency. Theoretically, the actual 
income from this particular form of capital as represented in 
the third column should be taxed, and afterward whatever is 
reinvested in some other form should earn remission of taxes. 
This method, while impracticable in such detailed application, 
might with advantage be applied to the taxation of an individ- 
ual's income as a whole. After all the individual components 
are combined — all the income elements, large or small, and all 
the outgo elements, including reinvestments — there will be a 
resultant net income for the individual which, and which alone, 
should be taxed. A system which would accomplish this 
would tax, to this individual, any net impairment of his capital, 
for such impairment would mean large income; but, on the 
other hand, if he were not depleting but laying up capital, it 
would exempt the increase, for such increase would not be part 



APPENDIX TO CHAPTER XVI 403 

of Ms income. Such a system would secure justice in the taxa- 
tion of income. It is practically what has usually been called 
the system of taxing " consumption." 

APPENDIX TO CHAPTER XVI 

§ 1 (to Ch. XVI, § 6) 

Mathematical Coeflficients of Probability, Caution, and Risk 

Let us call the riskless value V, the mathematical value V, 
the commercial value V", the coefficient of probability P, the 
coefficient of caution C, and the entire coefficient of risk H. 
We have, — 

P-^ -C-^' B-^' 

^-r ^-v' ^—v' 

Whence it follows that B = PC. 

That is, the total effect of risk on value is twofold: first, 
through mere probability, which gives mathematical value ; and 
secondly, through caution, which gives commercial value. 
Practically, it is usually impossible to separate P and C. The 
object of this analysis is not so much to introduce the caution 
factor explicitly, as to make the general distinction between B 
and P, and to point out that the actual market value of secu- 
rities is not their actuarial or simple " mathematical " value ; 
that, in other words, B is not the same thing as P. 

§ 2 (to Ch. XYI, § 7) 

Tormula for Mathematical Value of Risky Bond 

Let us denote by p^ the probability of receiving the first 
installment, a-^, of income due in one year, and hjp2 the prob- 
ability of receiving the second installment of income, ag, pro- 
vided the first year's is received, and again by pg the probability 
of receiving a^ in three years, provided the previous tivo have 
been received, and so on for j>4 . . . p„, where n is the number of 
years to the last payment. The chance of receiving the first 
payment is p^, hence the "mathematical value" of the first 
payment, when due, is aiPi, the present value of which is 

-i-^. But the chance of receiving the second payment is 
1 + i 



404 NATURE OF CAPITAL AND INCOME 

evidently not pa? but piP2 ; for one of the first principles of the 
theory of probabilities is that the chance of two successive events 
is the product of their successive probabilities. Thus, if the 
chance of heads appearing in coin tossing is ^, the chance of two 
successive heads is -^ x -|-, or \, and the chance of three succes- 
sive heads is, in like manner, ^ X ^ X |-, or -|-, etc. Hence the 
" mathematical value" of the second installment, a^, when due is 

a2PiP2, of which the present value is ^^ .A - In like manner, 
the mathematical present value of the third installment is 

(^zPxP^Pz ^ g^^(j gQ QQ_ rpjjg g^jj^ Qf ijJ^q expressions for present 
(1 + if 

value thus obtained is the total present mathematical value of 
the property. If we denote this mathematical value by F^, 
we have, — 

'^"' 1 + i "^ (1 + if (1+ if (1 + if 

If we suppose that all the probabilities are equal, we may 
denote all the jj's simply by p, and simplify by substituting p^ 
for P1P2, and p^ for PiPsPs? e^c. 

Since the p's represent the probability of receiving the in- 
stallments, it is clear that the chance or risk of not receiving 
them is the difference between this and unity. This risk of 
default we shall denote by the letter q. Thus, gi = 1 —pi, etc., 
and also p^ = 1 — q^, etc. If all the g's are equal, we shall de- 
note them by q, and the present value of the property may then 
evidently be written, — 
TT _ ai(l-g) I a2(l-qy' , asjl-qf , ■ a„(l-9)" 

1+i "^ (1 + if "^ (i + if ^•••^ (1 + 0"* 

In case the risk of default q is very small, it is evident that 

the fraction ^ is approximately equal to — . This may 

1 + i ^^ •" ^ 1 + i + q 

be seen by dividing the numerator and denominator of the first 

fraction by 1 — g, which will give for the new numerator unity, 

and for the denominator 1 + i + q -|-l-+-!£. In this expression 

1-g 

the fractional term becomes negligible when q is small, 

because the denominator, 1 — g, is approximately unity, 

while the numerator, g^ + iq, is made up of two terms, each of 



APPENDIX TO CHAPTER XVI 405 

whicli is the product of two very small quantities. Thus, if q 
is y^ and i is j^, the value of the fractional term becomes 
approximately .0005, which is a negligible quantity (compared 
with 1 + ^■ + g = l + .04 + .01). Hence when q is small, the 
formula for mathematical value becomes approximately, — 

XT d/ I ^ I ^ L. • . . _1_ ^™ 



1 + i + q (1 + i + qy {1 + i + qf (l + i^-g)" 

In other words, when the risk of default is small, its effect is 
substantially the same as that which follows from a rise in the 
rate of interest. If the rate of interest when risk is absent is 
4%, a risk of 1% will therefore merely increase the "basis" on 
which the loan can be contracted to about 5 % . Thus, if we 
recur to the so-called 5% ten-year bond, and suppose that 
the probability of each successive payment is -^^, and the 
risk of default, q, is y^, then the mathematical present value 
of the bond, when interest is 4^, is approximately, — 

Y = ^1 J ^ I ^ |_ etc 

= — + — ^ — -h— — + ,etc. 
1.05 (1.05)2 (1.05)3 ' 

In other words, the present value is approximately the same 

as the present value of a 5% bond on a 5% basis, which is of 

course par, or 100. 

But if the risk is great, the approximate formula given will 

no longer apply. Thus, if the chance of default is y^^-, or, in 

other words, if the chance of payment is only jL, the formula 

for the mathematical value of the property becomes, — 

TT _ ^IVT?) I ^2(to') I ^sCtW _t_ pf p 

l-h^ (1 + (1 + 
In this case it is evident that all terms after the first are neg- 
ligible compared with the first (unless the successive items a^, 
ag, etc., increase with sufficient rapidity to offset the decreasing 
fractions y^, y^Vo> ©tc). In the case of a 5 % ten-year $100 bond, 
in which the risk of default is at any moment ^, the approxi- 
mate value of the bond, obtained by omitting all terms after 

the first, would be _AllZ, or approximately 50 cents ! This 

" mathematical value " might be still further reduced by a co- 
ef6.cient of caution. In other words, the bond is worthless. In 



406 NATURE OF CAPITAL AND INCOME 

case of such high risk we cannot, therefore, apply the simple 
rule of adding to the rate of interest the rate of risk to obtain 
the "mathematical value"; and the "commercial value" 
would, of course, be even less than the mathematical value. 
In other words, it is practically impossible to compensate for a 
risky investment by increasing the rate of interest as though 
it were an insurance premium. In actual practice such a 
"bond" would be absolutely worthless; for, while the above 
calculations are correct on the basis of a chance of payment of 
one in ten, practically this chance of payment would be zero. 
The high risk not only makes the terms of the loan onerous, 
but these onerous terms make the uncertainty of repayment 
greater, and so on in a vicious circle. A lender who fancies he 
can offset a risk as high as -^-^ by lending only 50 cents instead of 
f 100 for a returnable principal of f 100^ will find that he has 
not offset that risk, but merely increased it. 

In the previous calculations, we assumed that a default in 
one payment carried with it a default in all subsequent pay- 
ments. We may, however, easily extend our formula to the 
general case by designating the chances of payment in succes- 
sive years, whether interdependent or not, by pi for the first 
year, p, for the second (instead of by p^ p^ as before), p^ for the 
third, etc., and changing the first equation on page 404 accord- 
ingly. 



§ 3 (to Ch. XVI, § 10) 

Variability about a Mean, as measured by the "Standard Deviation" 

Eor a more minute analysis of the bearing of chance it is 
preferable to measure the variability with reference to the 
mean. Thus, in the case mentioned, where the dividends are 
successively 5%, 5%, 6%, 5%, 5%, 4%, 5%, 7%, 5%, 3%, 
4%, 5%, instead of measuring the variability of dividends with 
reference to 5%, we should measure it with reference to the 
mean rate, which is 4.9%. The deviations from this mean 
during the twelve successive years were therefore: +0,1, 
+ 0.1, +1.1, +0.1, +0.1, -0.9, +0.1, +2.1, +0.1, -1.9, 
-0.9, +0.1. 



APPENDIX TO CHAPTER XVI 407 

A simple measure of the extent of variability displayed by 
such a series of deviations from the mean is what is called the 
" standard deviation. " This is a sort of average of the devia- 
tions — not the ordinary arithmetical mean, but the mean 
found by taking the arithmetical mean of the squares of the 
deviations and extracting the square root. The standard 
deviation which represents the above twelve individual devia- 
tions is thus, — 

+ (-1.9)2+ (-.9)-'2+ (.1)2 

(.1)2+ (.1)2+ (1.1)2+ (.1)2 + (.1)2+ (_.9)2+ (.1)2^ (2.1)2 ^ (.1)2 

12 
which is .95. 

This "standard deviation" is used instead of other averages 
for several reasons. The arithmetical mean of the deviations 
about the mean is quite unavailable, because, unless it be 
reckoned by disregarding all minus signs (in which case the 
result is an illogical makeshift), it is zero; the standard 
deviation is very readily calculated, not by performing the 
operations indicated above, but by recourse to a theorem 
that the mean of the squares of the deviations about the 
mean is equal to the mean of the squares of the deviations 
about any other magnitude less the square of the difference 
between the mean and this other magnitude. The proof 
of this theorem is simple, and may be found in the books 
on probability. Applying it to the illustrated case, we first 
take the deviations, not about the mean, but about some other 
magnitude, say 5%. These deviations are 0, 0, 1, 0, 0, — 1, 0, 
2, 0, - 2, - 1, 0. The squares of these are 0, 0, 1, 0, 0, 1, 0, 4, 
0, 4, 1, 0, of which the arithmetical mean is \^, or .902. This 
is the mean of the squares of the deviations about the mag- 
nitude 5. From this we are to deduct the square of the 
difference between the mean 4.9 and the other magnitude 5, 
about which the deviations were measured. The difference is 
.1, its square is .01. Deducting this from .902 we have .892 as 
the mean of the squares of the deviations about the mean. The 
square root of this is .95, which is therefore the standard 
deviation sought. Calculated by this method the standard 
deviation may usually be obtained in less than one tenth the 
time required by the direct method. 



408 NATURE OF CAPITAL AND INCOME 

The "standard deviation" plays an important role in the 
treatment of all statistics involving variation about a mean. 
One of its simplest uses is to change any given deviation into 
a deviation relative to the standard deviation (or to a fixed 
portion of it). This is usually done by dividing the absolute 
deviation by the standard deviation. Thus, in the above ex- 
ample, where the standard deviation is .95 %, an absolute devia- 
tion of, say, 2 % mean is a relative deviation of 2 -=- .95 or 
about 2.1. 

Such a reduction from absolute to relative deviation brings 
the different probability distributions or curves into a common 
comparison, so that probability tables may be constructed 
applicable to all. In one case the deviations may mean inches 
of rainfall, in another, pounds of barometric pressure, in an- 
other, the annual percentage of dividends, as in the case above. 
These are incommeasurable. But if each be compared with 
the standard deviation which applies to that particular case, 
and which would therefore be measured in inches, pounds, or 
annual percentages, respectively, we obtain three ratios which 
are simply pure numbers indicating the extent of the deviation 
compared with the standard deviation. 

If we now consult a probability table we may find at once 
what is the probability of any given relative deviation. For 
the chance that dividends will, in the case supposed, deviate 
in any given future year by 2 % from the mean rate of 4.9 % 
is, from the tables, 1 in 20; for the deviation, measured 
relatively, is, we saw, the number 2.1 and the probability cor- 
responding to this in the tables^ is If. This expresses the 
chance that the deviation will keep inside the limits of 2 % ; 
i.e. that the dividends will be between 2.9% and 6.9%. 

The wider the range of deviation considered, the less the 
chance that the actual dividends in any year will fall out- 
side that range. Moreover, the chance decreases far faster 
than the range increases. This relation, which follows from 
the theory of probability, has very important consequences in 

1 Thus on p. 55 of Davenport's " Statistical Methods," New York, 
Wiley, 1899, we find for a relative deviation 2.1, the number .4822 as the 
chance of the deviation in one direction. Hence the chance of the devia- 
tion in either direction is double this or .9644, about |f . 



APPENDIX TO CHAPTER XVI 409 

the theory of distribution. From it follows as a corollary that 
the richer an individual, the less risk in taking risks. Being 
possessed of capital, he has a wider range within which he can 
safely afford to operate, and therefore he has a far greater 
probability of keeping within these limits of safety than his 
less fortunate competitors. Professor Norton has also empha- 
sized the fact that the advantage of the capitalist is further 
enhanced by the tendency toward monopoly. " The result is a 
most interesting circle, constant combination at the top in 
order to force down the commercial price of the risk, and 
monopoly of the upper field, which pays tremendous profits, 
resulting in still greater increase in the financial power of the 
risk takers. To this there is no end, save in the divorce, 
through heredity, of ability and financial power." ^ 

An important application of these methods is to the calculation 
of the chance that earnings should fall below the amount re- 
quired to pay interest on bonds. This chance is found from the 
probability table. It is the probability corresponding to that 
relative deviation obtained by dividing the difference between 
the mean expected earnings and the interest by two thirds of 
the standard deviation. In this and other ways business men 
could, as Professor Norton has shown, make better use of their 
past experience than they do. Merely to glance over past 
earnings and receive an impression is not a very scientific mode 
of utilizing the facts which those earnings display. To aver- 
age them is not of much more value. While it is important to 
know the mean, it is also important to know the dispersion 
about the mean. This dispersion is shown by the standard 
deviation. The best procedure would therefore seem to be to 
calculate first the mean of past experience as to earnings; 
secondly, the standard deviation from that mean; thirdly, the 
chances of fluctuations thus displayed {e.g. the chance of 
earnings falling below the interest-paying line) ; and, fourthly, 
to correct the results thus obtained by taking into account the 
degree in which it is believed that the future will not follow 
in the footsteps of the past. Only the last of these four 
1 From a letter to the author. Cf. also Professor Norton's "Theory of 
Loan Credit," Publications of the American Economic Association, 1904, 
p. 54. 



410 NATURE OF CAPITAL AND INCOME 

operations need be done by rule of thumb. But at present 
all but the first and often even that are left to the merest im- 
pression. 

There was a time when business men did not use bond 
tables, when they did not calculate cost sheets, and even when 
life insurance was contracted for in scornful disregard of any 
mortality tables. Just as these slipshod methods have been 
displaced by the work of expert accountants and actuaries, so 
should the mere guessing about future income conditions be 
replaced by making use of the modern statistical applications 
of probability.^ 

§ 4 (to Ch. XVI, § 20) 

Method of computing a Pure Level Life Insurance Premium 

The chief peculiarity of life insurance is that each year's 
premiums, in properly organized insurance companies, are 
calculated not on the basis of the chance of death in that 
year, as in the case of fire insurance, but are computed as " level 
premiums," which exceed this chance in the early years of 
the policy, and fall short of it in later years. The wisdom of 
such an arrangement is justified by the incentive which 
is produced for all "risks" to remain insured, whereas when 
the "natural" premium only is charged, increasing with 
age, there is a tendency for the better risks to withdraw, 
making thereby a "selection" adverse to the companies. 
A consequence of a "level" premium being charged is that 
the policy acquires an increasing mathematical value with 
time, so that the policy holder, after a few years, sometimes 
possesses a very valuable property, which he can, if he chooses, 
sell or use as collateral security for loans, etc. The value of 
such a policy, computed on the mathematical basis, is of 

1 Cf. " The Put and Call," byL. E. Higgins, London, 1902, pp. 65, 66. 
For some suggestions along this line, see Edgeworth, " Mathematical 
Theory of Banking," Jour. Boy. Statis. Soc, March, 1888; for a state- 
ment of the modern statistical method, see Karl Pearson, Grammar 
of Science, and his journal "Biometrica" ; for an application of this 
method to financial and industrial problems, see J. P. Norton, Statis- 
tical Studies in the New York Money Market, New Haven (Tuttle, More- 
house & Taylor), 1903. 



APPENDIX TO CHAPTER XVI 411 

course the present value of the chance of receiving the insur- 
ance, less the present value of the chance of paying the 
premiums. Thus, for a man aged 30, who was insured 10 years 
before, the chance of his death at the age of 35 will be about 
g-lffo, or .86%, since of 84,720 living at age 30, about 732 die 
in their 36th year. Hence the present value of the chance of 
receiving his insurance of f 1000 in that particular year is 
^Ti" ' °^ $7.07, assuming the rate of interest to be 4%. In 
like manner we may determine the present value of the similar 
chance for every other year of possible life, and the sum total 
of these present values will be the total present value of the 
chance of receiving the insurance, $287.66. From this must be 
deducted the present value of the chance that he will pay' 
premiums. Thus, the chance of his paying the premium in the 
above-named year, when he is 35 years of age, will be the 
chance that he will be living at that time, which is .958. This 
multiplied by his premium and discounted gives the present 
value of this possible premium payment ; this added to the like 
sums for every other year will give the total present value of 
his obligation to pay premiums, $222.86 ; this, in turn, sub- 
tracted from the present value of the prospective insurance 
just obtained, namely $287.66, will give the present mathe- 
matical value of his property, $64.80, called the value of his 
insurance, or the "reserve" on his policy. 

The true "commercial value," or the value which he is will- 
ing to pay, will be somewhat higher. For, in this case, the 
coeflB-cient of caution operates to increase, not to diminish, the 
value of the property, as insurance tends, not to make a risk, 
but to reduce it. 

The calculation of mathematical values of life insurance has 
been very perfectly worked out. The reader who is interested 
will find the most complete explanations in the Institute of 
Actuaries' Text-book, 2 vols., London (Layton), 1901. 



INDEX 



Accounting, philosophical basis of, 
129, 140. See Capital accounts 
and Income accounts. 

Accumulation of interest : not in- 
come, but increase of capital, 
134-135, 224; results of, 224- 
226. 

Adornment, services of, 165. 

Agio sense of rate of interest, 195, 
247, 334. See Premium con- 
cept. 

Agriculture amenable to prediction, 
291. 

Amortization, definition of, 110, 332. 
See Depreciation fund. 

Amount of a sum, definition of, 203, 
329. 

Amusement, services of, 165. 

Annuity, regarded as income, 111; 
concept of interest based on 
perpetual, 191-194, on termi- 
nable, 194-195 ; capital-value of 
perpetual, 205-208 ; "deferred," 
207 ; examples of perpetual, 
208-209 ; capital-value of ter- 
minable, 209-210; examples of 
terminable, 210-211 ; the per- 
petual, taken as the standard 
income, 236-237 ; sinking fund 
based on difference between in- 
come and ideal terminable, 
243-244 ; depreciation fund 
based on difference between 
actual income and ideal per- 
petual, 243-244 ; mathematical 
formula for present value of 
perpetual, 369 ; formulas and 
diagrams of capital-value of, 
payable annually, semi-annually, 
etc., 369-371; formulas for 
capital-value of terminable, 374- 
378 ; taxation of terminable, 
in England, 401. 

Appraisal of labor, 172. 



Appraisal of wealth, methods used 
in, 11-12, 34-36; based on 
future worth, 204-205. 

Appraised price, 13 ; a source of 
inaccuracy in measurement of 
wealth, 16-17; discrepancies 
between, and actual selling price 
(of shares in stock company), 
70-72. 

Apprenticeship considered as an 
investment, 169-170. 

Area method of representing income, 
207-208, 371-374. 

Assets, definition of, 67-68, 329; 
discrepancies in valuation of, 
71-72 ; effect of increase or 
decrease in value of, 73-74; 
fraudulent methods of swelling, 
74 ; relation of stability of, to 
capital-balance necessary for 
safety of a business, 81 ; cash, 
quick, and slow, 82 ; true value 
of liabilities derived from, 84- 
85, 139 ; items of, to be included 
in capital and income accounts, 
139-140 ; methods employed for 
obtaining valuation of bank 
(discount paper, short-time 
loans), 194-195, 198-199, 204; 
effect of chance element on value 
of, 287-288 ; figures of, of life 
insurance companies, 295. 

Assignment, settlement of bank- 
ruptcy by, 86. 

Austria, taxation of forest lands in, 
254. 



Balances, method of: in summing 
capital or income accounts, 90- 
91, 142-143, 183, 335; taxation 
by, 97-98 ; contrasted with 
method of couples in income 
summation, 157-158. 

Balance sheet, definition of, 329. 



418 



414 



INDEX 



Balance sheets, to show accumula- 
tion of surplus, 69 ; effect on, of 
increase or decrease in value 
of assets, 73-75 ; interdepend- 
ence of, of different firms or 
companies, 87-92 ; to show 
methods of balances and couples, 
91 ; to show distinction between 
accounting of real and of fic- 
titious persons, 93-94 ; prospects 
of businesses shown by, 264. 

Bank deposit rights, wealth under- 
lying, 27. 

Bank notes, wealth underlying, 27; 
nature of property right in, 32, 
280 ; legal regulations govern- 
ing, to avoid risk, 289. 

Bank reserves, risk-meeting function 
of, 290. 

Bankruptcies, communication of, 
87-88. 

Bankruptcy, state of, 82 ; laws re- 
lating to, 83 ; bondholders' and 
stockholders' position in case of, 
83-86; settlement of, 86; rela- 
tion of general crisis to indi- 
vidual, 297. 

Banks, national : liability of stock- 
holders in, 83 ; investments of, 
in government bonds, 280-281. 

Basis of a security, definition of, 329. 

Bemis, Edward W., cited, 39. 

Bequests not counted as income, 109. 

BernoulU's Theorem, 267, 275. 

Bills of exchange, 204-205. 

Bohm-Bawerk, quoted on attempts 
to define "capital," 53-54; con- 
cept of capital of, 56 ; cited, 
60 n.^; statement that interest 
is not an element in cost of 
production, 173-174 ; cited in 
connection with productivity 
theory, 187 ; concept of interest 
of, 195, 247 ; on interactions as 
preparatory to enjoyable serv- 
ices, 318. 

Bondholders, nature of rights of, 
31-32, 85 ; distinction between 
stockholders and, 85, 288-289; 
position of, in reorganization 
after bankruptcy, 85-86; rela- 
tion of, to risks of enterprises, 289. 

Bonds, wealth underlying property 
in, 25, 26; nature of rights of 
holder, 31-32, 85; capital-value 
of, 211-217, 382; realized vs. 



earned income of, 231-236; 
application of depreciation fund 
to, 242-243 ; as investments, 
277-281 ; formulse for comput- 
ing value of, 378-382 ; formula 
for mathematical value of risky, 
403-406. 

Bond value books, 213-215. 

Bougand, quoted, 168 n. 

Branford, Victor, cited, 63 n. 

Building and loan association, in- 
come accounts of, 127-128. 

Bullock, C. J., definition of income 
by, 349-350. 



C 



Call, option known as a, 298. 

Campbell, A. C, cited on moral 
effects of insurance, 295 n. 

Canard, human beings counted as 
wealth by, 5 n.^. 

Cannan, Edwin, definition of wealth 
by, 3 ; cited on definition of 
capital, 56, n.^ ; cited in connec- 
tion with wage fund theory, 59 ; 
use of term "capital" by, 60 
and n.^ ; on concept of income, 
102 n.^; savings regarded as 
income by, 108; concept of 
income of, 116; on distinction 
between rent and interest, 186 
n.^; confusion of earned with 
realized income by, 247-248. 

Capital, concept of, as stock of wealth 
at an instant of time, 51-52, 
324 ; varying views of, 53-57 ; 
relation of labor to, 55 ; viewed 
as productive, 56 ; fancied dis- 
tinction between land and, 56 n.^ ; 
errors resulting from narrow 
interpretations of, 57-58 ; rela- 
tion of author's definition to 
established usage, 60-61 ; dic- 
tionary definitions of, 61-62 ; 
business men's view of, 63-65 ; 
two senses of, called capital- 
goods and capital-value, 66-67 ; 
relation of surplus or undivided 
profits to, 68-70; original and 
net, 69, 330; bookkeeper's vs. 
market's estimate of, 70-72 ; 
four separate meanings of term 
applied to person or firm, 72 ; 
classification of, 72 ; nominal 
and paid-up, 72, 330; payment 



INDEX 



ill 



of dividends out of, 75, 256 ; 
of "real" person and of "fic- 
titious" person, 92-93; relation 
of credit to, 96 ; fallacious sta- 
tistics of, 98 ; confusion of in- 
come and, 105-112, 114-115, 
351 ; fallacy of adding to income 
savings of, 108, 134-135, 247- 
255, 349, 353 ; income need not 
leave unimpaired, 110-111 ; 
outgo is not, 124; analogous to 
and correlative with income, 
184; physical productivity and 
value productivity of, 185, 186 ; 
physical return and value return 
of, 185, 186; mistake of dis- 
tinguishing between land and, 
186-187 ; fundamental principle 
of value of (value of future 
income), 188 ; increase of, equals 
excess of earnings over income, 
237-238 ; relation between 
amount of, and risk involved, 
277, 408-409; reserves of, held 
to avoid risk, 290 ; representa- 
tion of income and, by polar 
coordinates, 393-395 ; effect of 
foreknown tax on increase of, 
398-400; taxation of impair- 
ment of, 400-403. 

Capital accounts, definition of, 67, 
89 ; methods of balances and 
couples in summing up, 90-92; 
relation between income ac- 
counts and, 139, 256-264. 

Capital balance, 81, 329. 

Capital cost, 124-125. 

Capital curves, 303-322, 369-378. 

Capital-goods, meaning of term, 67, 
329 ; classification of, 72. 

Capital instruments, 66-67, 72, 329 ; 
regulation of income by com- 
bining, 127-129, 245-246. 

Capitalization, definition of, 64, 330 ; 
rate of, 194; employment of 
rate of, as alternative to rate 
of interest, 199 ; table showing 
equivalent rates of interest, 
discount, and, 200; of income 
by means of rate of interest, 202 : 
dimensions of rates of discount, 
interest, and, 367-368. 

Capitalize, use of term, 64, 330. 

Capital property, 67, 72, 330. 

Capital-value, 67, 72, 327, 330 ; deter- 
mination of, from rate of inter- 



est, 202 ; of perpetual annuity, 
205-208, 369 ; of terminable 
annuity, 209-210, 374-378 ; risk 
element in determining, 210; 
of a bond, 211-217, 382; of 
any income stream, 217-221, 
387-388; of alternative income 
streams, 221-222 ; of group of 
articles, 223 ; is the discounted 
value of expected income, 223- 
224, 304-305; less than total 
expected income, 227-228 ; effect 
of change of interest rate on, 
229, 271-273, 390-393 ; enmner- 
ation of causes affecting, 284- 
285 ; as mean between past cost 
and future income, 305-309 ; 
formula for, of sum due in one 
year, and of sum due at any time, 
368. 

Capital-wealth. See Capital goods. 

Carver, cited, 117 n.^. 

Cash, income and outgo accounts of, 
131-132, 135-136 ; account book 
of lawyer, 136-137 ; as an in- 
come meter, 137-138. 

Caution, coefficient of : 276-277, 330 ; 
applied to insurance, 292 ; mathe- 
matical presentation of, 403. 

Census (U. S., 1905), cited concern- 
ing railway valuation, 36 n. 

Certificates, of property, 23 ; ne- 
cessity of separating from wealth, 
property, services, and utility, 
38; stock, 68-70; receiver's, 
86. 

Chance, element of, in property 
rights, 22, 330; involving risk 
of insolvency, 81 ; nature of, 
265-269 ; always an estimate, 
266 ; an affair of ignorance, 
268; measurement of, 269-271; 
mathematical value of a, 275; 
in valuing stock, 280-283 ; effect 
of, on discount curve, 286-287 ; 
effect of, on bookkeeping, 287- 
288 ; effect of, on capital curves, 
320-322. 

Chen, Chin tao, cited on utility, 47. 

Clark, J. B., cited on utility, 47; 
concept of capital of, 55, 56, 
60; term "capital-goods" sug- 
gested by, 67 ; use of economic 
terms by, 67; "Niagara Falls" 
simile of, applied to income, 129 ; 
distinction between work and 



416 



INDEX 



labor drawn by, 175 n. ; con- 
cept of interest of, 247. 

Clothing, services of, 165. 

Coefficients of caution, probability, 
and risk. See Caution, etc. 

Combination of capital instruments 
to standardize income, 127-129, 
245-246. 

Commodities, definition of, 5, 323, 
331 ; classification of, 7 ; error of 
reckoning as income, 105-106. 

Complete rights to property, 36-37, 
95-96, 324-325, 335. 

Composition, settlement of bank- 
ruptcy by, 86. 

Computation tables, 243 n., 283- 
284, 408-411. 

Consumption, 145, 152, 164, 165, 336, 
350. 

Contingent liability, 83. 

Control, value of, as applied to 
railway ownership, 35-36. 

Copyright, wealth underlying, 27, 
29. 

Cost, included in term "outgo," 120; 
influence of past, on present 
value, 188-190. 

Cost of production, 151, 173-174, 
184. 

Cotgrave, definition of capital by, 
62. 

Couple, definition of, 331. 

Couples, method of ; in capital sum- 
mation, 90-91, 183-184, 335; 
applied to accounting of rail- 
way company, 94 ; taxation by, 
97-98; income summation by, 
143-152, 183-184, 335; natural 
income discovered by, 150-151 ; 
contrasted with method of bal- 
ances in income summation, 157- 
158. 

Courcelle-Seneuil, use of term "capi- 
tal" by, 60. 

Credit, nature of property right 
represented by, 32-33 ; mis- 
taken view of, 39 ; relation of, 
to capital, 96-97 ; in the sense 
of an item of a transaction, 158- 
159, 336. 

"Credited," income said to be, 122, 
132, 325. 

Creditors, regarded as risk-takers, 
83-84 ; bondholders contrasted 
with stockholders as, 85. 

Crises, causes of, 296-297. 



Currency inflation, mistaken idea 

the basis of, 38-39. 
Custom (tailor's), wealth represented 

by, 29. 



D 



Daniels, use of term "capital" by, 
60 n.''. 

Dargun, human beings counted as 
wealth by, 5 n.^. 

Davenant, on human beings as wealth, 
5 n.2. 

Davenport, "Statistical Methods" 
by, 408 n. 

Debit, an item of a transaction, 122, 
132, 158-159, 336. 

Debt, imprisonment for, 83 ; repu- 
diation of, 84; payments on 
(interest or principal) are outgo, 
134. 

Definition, tests of a, 116. 

De Foville, use of term "capital" 
by, 60. 

Depletion of capital, not to be de- 
ducted from income, 110, 134; 
taxation and, 400-403. 

Depreciation not outgo, 234. 

Depreciation fund, regulation of in- 
come by, 125-126, 239-243; 
geometrical figures representing, 
240, 241. 

Depreciations, item of, in income and 
capital accounts, 257-263. 

Desirability, concept of, 41, 326; 
discussion of term, and term 
"utility," 42-43. See Utility. 

Dimension, definition of, 331. 

Dimensions : wealth, price, and value, 
3-15, 341-344; of income- 
capital ratios, 186, 357 ; of rates 
of interest, discount, and capi- 
talization, 367-368. 

Discommodities, class of articles 
termed, 120. 

Discount, rate of, 199, 200, 327, 332 ; 
table showing equivalent rates 
of interest, capitalization, and, 
200; total, on a sum, 209-210, 
331 ; mathematical relations 
between rates of interest and, 
364-366; between rates of, 
for different time reckonings, 
366-367 ; dimensions of rates 
of interest, capitalization, and, 
367-368. 



INDEX 



417 



Discount curve (Exponential curve), 
203-204, 223-224, 331-332; ap- 
plications of, 206-208, 272, 284- 
287, 303-309, 317-322, 360-361, 
378, 380-381, 391-394. 

Discount paper, banks', 204. 

Disservices, definition of, 20, 119- 
120, 325, 332; eniuneration of, 
120; measurement of, 120-121; 
examples of, 123; "necessary 
evils," 123; one phase of, and 
services termed "interactions," 
144; transformations of wealth 
from one point of view are, 146. 

Distribution curve of incomes, 142. 

Distribution ledgers, 142, 143. 

Disutility, criticism of term, 42. 

Dividends, effect of payment of, 
on capital account, 75 ; payment 
of, out of capital, 75, 256 ; 
variability of, 281-282, 406- 
407. 

"Doses" of capital, 185. 

Double counting, fallacy of, in con- 
cept of income, 107-108, 113- 
115, 116, 347, 350; economists' 
attempts to avoid, 109-112. 

Double entry bookkeeping, 144, 159, 
325-326. 

Double taxation, 39, 97-98, 250-253, 
255. 

Du Cange, Dufresne, definition bf 
capital by, 62. 



E 



"Earning power" of stock, 71. 

Earnings (Earned income), defini- 
tion of, 234, 333 ; distinction 
between realized income and, 
234-236, 247-253, 327-328, 353 ; 
excess of, over income, equals in- 
crease of capital, 237-238, 328. 

Edgeworth, F. Y., definition of in- 
come by, 102 n.' ; cited, 410 n. 

Elements of income or outgo, 121. 

Emery, H. C, cited on speculations, 
300. 

Endorsement, influence of, in re- 
ducing risk, 289. 

Engel, human beings counted as 
wealth by, 5 n.^, 17. 

England, bankruptcy laws in, 83 ; 
income taxation in, 253, 401. 

Enjoyable income, 105, 112-113, 
118, 325-326. 

2e 



Enjoyable objective services ("Con- 
sumption"), enumeration of, 
165. 

Exchange of wealth, 10, 11, 22, 149, 
332 ; analysis of an, 158-159. 

Expense, definition of, 119-120, 332. 

Exponential curve. See Discount 
curve. 

F 

Factor's agreement, property right 
represented by, 28. 

Fee simple, rights in, 23 ; wealth 
underlying, 26; definition of, 
37 ; an asset having no counter- 
part liability constitutes a, 95. 

Fetter, F. A., cited on utility, 47; 
definition of capital by, 55 ; cited 
on confusion between quantity 
and value of wealth, 56 n.^; 
use of term "capital" by, 60 
n.^; use of economic terms by, 
67; concept of income of, 117, 
165, 350-351 ; on distinction 
between rent and capital, 186 n.*^. 

Fictitious person, definition of, 335; 
accounting of, distinguished from 
that of real person, 92, 138-139, 
153, 160-161. 

Finished products, classification of, 7. 

Flow, definition of a, 332. 

Flow of wealth, income conceived 
as a, 51-52, 101 ; duration of, 
52; rate of, 52, 332. 

Flux, use of term "capital" by, 60; 
concept of income of, 117. 

Forecasts, of income from capital, 
283-284; by trade journals, 
291 ; speculators experts in, 
295 ; crises caused by a general 
error in, 296-297. 

Foreclosure, settlement of bank- 
ruptcy by, 86. 

Forests, appraisal of present value 
of, based on future worth, 205 ; 
taxation of, 254. 

France, limited liability in, 83 ; 
taxation of forest lands in, 254; 
government bonds in, 281. 

Franchise rights, wealth underlying, 
26, 29. 

Franklin fund, accumulation of 
interest shown by, 225. 

Fund, definition of a, 332. 

Fund of wealth, capital conceived 
as a, 51-52. 



418 



INDEX 



Future, value of any capital-good 
dependent on the, 188-199, 204- 
205, 223-224; estimates of, 
based on the past, 283-284, 291, 
295, 296-297. 

Futures, trading in, 298-300. 



G 



Gambling, uneven value of the 
chances in, 275 ; distinction be- 
tween speculation and, 295. 

Gaskill, Alfred, quoted on taxation 
of forest lands, 254. 

General property tax, 253. 

George, Henry, proposition of, to 
nationalize land, 30-31. 

Germany, appraisal of forests in, 
205 ; taxation of forest lands in, 
254. 

Gibbs, J. W., quoted, 65 n.^. 

Gide, use of economic terms by, 43. 

Giffen, use of term "capital" by, 60. 

Gold certificates, nature of property 
right in, 32. 

Goods : wealth, property, and serv- 
ices treated under term, 41, 327 ; 
not income, 351. 

Good will, wealth underlying rights 
of, 27, 28-29. 

Government bonds, 31-32, 280-281. 

Government property, wealth under- 
lying, 27. 

Government reports, reduction of 
risk by, 291. 

Government's taxing power, nature 
of, 30. 

"Graveyard insurance," 294. 

Gross income, definition of, 121, 333. 

Guaranties, method of, to avoid 
risk, 288-289. 

Guth, Franz, on income, 356. 

Guyot, use of term "capital" by, 60. 



H 



Hadley, A. T., " capital " according 
to, 60 n.^ ; concept of income of, 
117; on commutation of risks, 
289, 299. 

Health as wealth, 176. 

Hedging, shifting risks by, 299-300. 

Hermann, F. B. W. v., concept of 
capital of, 54, 56 ; perishable 
goods regarded as non-capital 
by, 63 ; on income, 352-353. 



Hicks, use of term "capital" by, 61. 

Higgins, L. R., cited, 410. 

Hire, rights of, wealth underlying, 26. 

Holland, T. E., cited concerning 
definition of "rights," 21. 

Housing and warming, services of, 
165. 

Human beings, considered as a form 
of wealth, 5, 17 ; classification of, 
in scheme of wealth, 7. 

Human body, transformation of 
services through, 167—168; effect 
of condition of, on subjective 
and objective income, 175-176. 



Ignorance, element of, in chance, 268 ; 
reduction of risk by decrease of, 
291. 

Immaterial wealth, items included 
under, 4 ; disadvantage of the- 
ory of, 39. 

Impairment of capital, 110, 134, 
328; taxation of, 400-403. 

Imprisonment for debt, 83. 

Income, concept of, as flow of serv- 
ices during period of time, 51— 
52, 101, 116-118, 324; savings 
not to be included in, 108, 134— 
135, 247-255, 349, 353; vary- 
ing concepts of, 101-115, 345- 
356; conceived as money-in- 
come, 103-104, 115, 117-118, 
333; obtained in kind, 104; 
real, 104-106, 112-113; enjoy- 
able, 105, 112-113, 333; serv- 
ices only to be regarded as, 
106-107, 112, 116-118; fallacy 
of double counting in concept of, 
107-108, 113-115, 116, 347, 
350; not "regular," 109; stand- 
ard, 110, 234, 236-237, 328, 
333, 396-398 (see Standard 
income) ; need not leave capital 
unimpaired, 110, 328; needless 
distinctions between social and 
individual, 113-115; confusion 
of capital and, 114-115, 351; 
primary or natural, 115, 150, 
333; social, 116, 141, 333, 348; 
net, 118, 121, 130-131, 333 
(see Net income) ; use of term, 
in two senses (services and value), 
121 ; element of, 121 ; gross, 
121, 333 ; viewed from one point 



INDEX 



419 



is outcome or yield, 122 n. ; 
effect of depreciation fund on, 
125-126, 238-243; other meth- 
ods of steadying, 127-129, 243- 
247, 259-263, 293-294 ; methods 
of reckoning real person's (law- 
j^er's) and fictitious person's 
(railway corporation's), 130-139 
(.see Income accounts) ; total 
social, 141 ; distribution of, 
142-143; objective, 165; ob- 
jective and subjective final stage 
of, 165-169; psychic (subjec- 
tive), 167-169, 177, 333 ; capital 
analogous to and correlative 
with, 184; value of capital 
derived from future, 188; pur- 
chasing power over, 191 ; pay- 
able annually and semi-annually, 
192; line method of represent- 
ing, 206-207, 371-372; area 
method of representing, 207- 
208, 371-374 ; determining capi- 
tal-value of, 217-221 ; case of 
capital-value less than total ex- 
pected, 227-228; realized vs. 
earned, 231-236, 238, 247-255, 
327-328, 353 ; perpetual annuity 
taken as the standard, 236-237 ; 
regulation of, by repair fund, 
259-263 ; risk as applied to im- 
mediate, 275-276; forecasts of, 
283-284 ; effect of changes in, on 
capital- value, 284-285 ; insurance 
a means of steadying, 293-294; 
increase of value is not, 351 ; 
diagrams for continuous and 
discontinuous, 371-374; repre- 
sentation of capital and, by 
polar coordinates, 393—395 ; two 
rival concepts of standard, when 
interest rate varies, 396-398. 
Income accounts, services and dis- 
services which enter into, 119- 
121 ; for house and lot, 122-126 ; 
of building and loan association, 
127-128; of lawyer (real per- 
son), 131-134, 135-136, 163, 
174-175 ; of railway corpora- 
tion (fictitious person), 138- 
139; relation between capital 
accounts and, 139, 256-264, 325 ; 
items of assets and liabilities 
to be included in, 139-140, 
325; of society as a total, 141- 
142; of United States, 142- 



143 ; entrance of interactions 
into, 143-145, 325; of logging 
camp and sawmill, to illustrate 
application of method of couples, 
152-154 ; of dry goods company, 
to illustrate double entry book- 
keeping, 159-162; of factory 
company, to show relation be- 
tween capital accounts and, 
258-262 ; siunmarized definition 
of, 333. 

Income and outgo accounts, 122- 
140. *See Income accounts. 

Income bonds, 85. 

Income meter, "cash" in income 
accounts termed an, 137-138. 

Income-services, 121. 

Income summation, by method of 
balances, 90-91, 142-143, 183, 
335 ; by method of couples, 
143-152, 183-184, 335; method 
of couples contrasted with 
method of balances in, 157— 
158. 

Income tax, 250-253, 398-400 ; effect 
on capital of misconceived, 
253-254 ; unrestricted applica- 
tion of, impracticable, 400-403. 

Income-value, 121, 327, 333 ; rate of 
interest a link between capital- 
value and, 202, 327-328. 

Individual income, distinctions be- 
tween social and, 113—115. 

Insolvency, 81 ; true and pseudo, 82. 

Installment, payment by, as a means 
of regulating income, 127, 244— 
245. 

Instrument of wealth, 5, 19, 333. 

Insurance, origins of, 275-276 ; avoid- 
ance and shifting of risks by, 
288, 291-294; a means of 
steadying income, 293-294 ; 
various forms of, 294. 

Insurance companies, identity of 
creditors and stockholders in 
mutual, 85 ; terminable annuities 
used by, 210 ; bonds offered by, 
217; forecast of interest rate 
by, 274. 

Interactions between two instru- 
ments or groups of instruments, 
144, 325, 334; formerly styled 
"productive services," 145; 
three classes of (transformation, 
transportation, and transfer), 
145-152; natural services of 



420 



INDEX 



capital consist of, 152-156 ; 
shown by diagrams to be prepara- 
tory to enjoyable services, 317- 
320. 

Interest, is capital and not income, 
134-135, 224 ; not an item in cost 
of production, 173-174 ; spurious 
distinction between rent and, 
186-187 ; crude theories of, 187- 
188; nominal principal and, 
in case of bond, 211-212, 215, 
217 ; accimaulation of, 224-226 ; 
definition of nominal and total, 
334. 

Interest, rate of: defined, 191, 
334; various meanings of, ac- 
cording to frequency of pay- 
ment, 192-194, 334; payable 
annually and semi-annually, 192 ; 
premium and price concepts 
of, 194-196, 246; interchange- 
ability of premium and price 
concepts of, 196-199; table 
showing equivalent rates of dis- 
count, capitalization, and, 200; 
a link between capital- value and 
income- value, 202, 327 ; table 
of, realized per annum on three, 
four, and five per c ent bonds, 2 1 4- 
215; effect on capital-value of 
change in, 229, 271-273, 390- 
393 ; value-return may be greater 
or less than, 229-234; risk as 
applied to, 271-274 ; forecast of, 
by insurance companies, 274; 
riskless, mathematical, and com- 
mercial, 279-280; on govern- 
ment bonds, 280-281 ; mathemat- 
ical relations between annual, 
semi-annual, and quarteriy rates 
conceived in price sense, 357- 
358, in premium sense, 358- 
362 ; mathematical relation be- 
tween, and rate of discount, 
364-366 ; dimensions of, and 
rates of discount and capitaliza- 
tion, 367-368 ; variation of, 
produces two rival concepts of 
standard income, 396-398. 

Interstate Commerce Commission, 
Report of, cited, 39. 

Inventory, distinction between quan- 
tity, price, and value of wealth 
shown in an, 14. 

Investments, classification of, as 
safe and unsafe, 277; relation 



between amount of capital and 

risk of, 277, 408-409. 
Irredeemable paper money, wealth 

underlying, 27; nature of, 30. 
Item of wealth, 5, 337. 



James, William, quoted, 168 n. 

Jevons, W. S., use of phrase "final 
utility" by, 46; concept of 
capital of, 54, 57; use of term 
' ' discommodities ' ' by, 1 20 ; 
cited on rent entering into cost 
of production, 173. 

Joint stock companies, capital ac- 
counts of, 68-70; limited Ua- 
bility in, 82-83 ; shares in, as 
example of perpetual annuities, 
209. 

Joint stock rights, wealth underlying, 
26. 

Juglar, cited on crises, 296. 

K 

Kind, income obtained in, 104. 
Kleinwachter, concept of capital of, 

54; raw materials regarded as 

non-capital by, 63 ; on income, 

102, 351-355. 
Knies, on capital, 54, 57, 60. 
Knowledge, reduction of risk by 

method of increasing, 288, 291 ; 

utility of speculation based on, 

298. 
Komorzynski, on capital, 65 n.^. 



Labor, economists' views of relation 
between capital and, 55 ; de- 
fined as outgo in form of htunan 
exertion, 120, 334; as form of 
disservice, 145 ; appraisal of, 
172 ; in a sense the only true 
cost of production, 175 ; dis- 
tinction drawn between work 
and, 175 n. 

Labor power, 316-317. 

Lafrentz, L. W., use of term "capi- 
tal" by, 63. 

Land, regarded as one class of wealth, 
5, 334 ; classification of, 7 ; 
nationalization of, 30—31, 254; 
fancied distinction between capi- 
tal and, 56 n^ ; view of, as non- 



INDEX 



421 



capital by classical economists, 
63; mistake of distinguishing 
between capital and, 186-187; 
an example of capital yielding 
an approximately perpetual 
annuity, 209 ; determination of 
uses of, 221 ; benefits of specu- 
lation in, 222 ; taxation of, 254. 

Land improvements, 5, 7, 334. 

Landry, time element in concept of 
capital of, 57. 

Lawyer, income and outgo accounts 
of, 131-137, 162-164, 174-175. 

Lease, wealth underlying rights of, 
26, 34-35. 

Liabilities, definition of, 67, 325, 334 ; 
relation of capital-balance to, 
looking to safety of a business, 
81 ; true value of, derived from 
assets, 84-85, 139; consideration 
of, in income and outgo accounts, 
134-135, 139-140, 162-164. 

Liability, limited and contingent, 
82-83. 

Life insurance, steadying of income 
by, 294, 295; method of com- 
puting pure level premiima, 
410-411. 

Limited liability, in case of joint 
stock company, 82-83. 

Line method of representing income, 
206-207, 371-372. 

Liquidation, resulting from bank- 
ruptcy, 86 ; a crisis defined as a 
time of general and forced, 296. 

Loans, short-time : interest in case 
of, 194-195, 198-199; rate of 
discount employed for, 199, 204. 

Logging camp accounts, 152—157, 318. 

Lowell Institute, possibilities of 
accumulation shown by, 225. 



M 



MacCulloch, on human beings as 
wealth, 5 n.2; concept of capital 
of, 55 ; quoted on wage fund 
theory, 59. 

Machines, offsetting of depreciation 
in, 241-242. 

MacLeod, H. D., definition of wealth 
by, 4 ; concept of capital of, 55 ; 
includes credit under capital,. 96. 

Marginal utility (desirability), defi- 
nition of, 46, 331 ; mathematical 
expression for, 344-345. 



Marshall, Alfred, use of economic 
terms by, 43, 46, 61 ; treatment 
of capital by, 54 ; on distinction 
between capital and non-capital, 
57 ; on concept of income, 1 14, 
117, 347-348; on avoidance of 
double counting in concept of 
income, 114; on transformation 
of wealth, 145. 

Marx, distinction between capital 
and non-capital according to, 
55 ; on relation between capital 
and labor, 55 ; denies that 
capital is productive, 56. 

Measurement of psychic income, 
177. 

Measurement of services and dis- 
services, 19-20, 120-121. 

Measurement of wealth, by quan- 
tity, 8-9; by price, 9-11; by 
value, 13-14; inaccuracies in, 
15-17 ; expressed mathematic- 
ally, 341-344. 

Methods of avoiding risk. See 
Risk. 

Methods of balances and couples. 
See Balances and Couples. 

Methods of standardizing income, 
125-129, 243-247, 259-263, 
293-294. 

Meyer, R., on income, 355-356. 

Mill, J. S., distinction between capi- 
tal and non-capital by, 54 ; 
capital itself regarded as a 
product by, 55 ; quoted on 
wage fund theorj^, 59. 

Miner's inch, 193, 208-209. 

Mines, terminable income exemplified 
by, 209, 210. 

Mixter, editor of Rae's Sociological 
Theory of Capital, 65 n.i. 

Money, uniformity of measurement 
by means of, 15 ; irredeemable 
paper, 27, 30 ; distinction be- 
tween three elements (wealth, 
property, certificates) to which 
term is applied, 38. 

Money-income, concept of, 103-104, 
115, 117-118. 

Money price, 335. 

Money value, 337. 

Money-wages not real wages, 104. 

Monopoly, effect of tendency toward, 
on risk element, 409. 

Monopoly franchise, wealth under- 
lying rights of, 25, 27, 29. 



422 



INDEX 



Mortgage, use of, to maintain regu- 
larity of income, 127, 244-245 ; 
reduction of risk by, 289. 

Murray, J. A. H., dictionary definition 
of income, 62-63, 345-346. 

Mutual insurance companies, credit- 
ors and stockholders identical 
in, 85. 



N 



National banks, liability of stock- 
holders in, 83 ; government 
bonds bought by, 280-281. 

Natural income, 118, 150; ascertain- 
ing, by method of couples, 150- 
151. 

Nau, Carl H., cited, 39. 

Net capital, 69, 330. 

Net income, 118, 121, 130-131, 333; 
example of, in case of lawyer, 
136-137, 163, 174-175; lacking 
in case of fictitious persons, 
138-139; of society, 141-143; 
determining by method of bal- 
ances and method of couples, 
157-158; of merchant's stock, 
223. 

Net outgo, definition of, 121, 335. 

Net product, social income conceived 
as society's, 113-115. 

Nicholson, J. S., human beings 
counted as wealth by, 5 n.^ 
use of term "capital" by, 61 
on credit as "revenue capital, 
96. 

Norton, J. P., on relation between 
am.ount of capital and risk in- 
volved, 277, 409; on use of 
probability computations, 283 
n.i, 410 n. 

Notes, wealth underlying, 26, 28. 

Nourishment, services of, 165. 



O 



Objective cost of production non- 
existent, 173. , 

Objective income, 165-169; points of 
divergence of, from subjective 
income, 169-176. 

Ofner, human beings counted as 
wealth by, 5 n.^. 

Ophelimity, 42. 

Options, stock exchange (puts and 
calls), 298-299. 



Out-come, income viewed from one 
point becomes, 112 n. 

Outgo, definition of, 119, 326, 335; 
element of, 121; net, 121, 335; 
use of, in two senses (disservices 
and value), 121 ; viewed from 
one point is ingo, 123 n. ; not 
capital, 124; offsetting of, by 
depreciation fund, 125-126 ; 
method of couples applied to, 
151-152; depreciation is not, 
234. 

Overvaluation of capital, 79-80. 

Owner-method of taxation, 97-98. 

Ownership, meaning of, 18 ; partial 
and total, 34-36, 95-96, 324- 
325, 335 ; change in forms of, in 
reorganization after bankruptcy, 
86 ; credit a form of divided, 
96-97 ; proper determination 
of, in taxation of property, 97— 
98; change of, 149-152, and see 
Exchange and Transfer. 



Palgrave, definition of capital by, 62. 

Panama Canal, example of depend- 
ency of capital-value on future 
services, 188-189. 

Panics, causes of, 296-297. 

Pareto, human beings counted as 
wealth by, 5 n.^; introduction 
of term "ophelimity" by, 42; 
cited on utility, 47; use of 
term "capital" by, 60; dis- 
tribution curve of incomes of, 142. 

Partial rights to property, 34-37, 95- 
96, 335. 

Partnership, wealth underlying rights 
in, 26 ; liability of members of a, 
83 ; income considered in re- 
spect to, 130. 

Patent rights, wealth underlying, 27. 

Payment by installment a means of 
regulating income, 127, 244-245. 

Pearson, Karl, cited, 410 n. 

Pension, the diminishing capital- 
value of a, 238-239. 

Person, fictitious and real, defined, 
335. See Fictitious and Real 
persons. 

Petty, on human beings as wealth, 
5 n.2, 17. 

Physical productivity of capital, 185, 
186. 



INDEX 



423 



Physical return of capital, 185, 186. 

Piecework, terms used in measure- 
ment of, 19-20. 

Pierson, N. G., definition of income 
adopted by, 102 n.\ 346. 

rigou, cited on utility, 47. 

Pitt, on sinking fund, 243. 

Pocket cash, risk-meeting function 
of, 290. 

Polar coordinates, representation of 
capital and income by, 393- 
395. 

Practice (physician's), wealth repre- 
sented by, 29. 

Prediction. See Forecast. 

Preferred stock, 85 ; share of, to 
illustrate riskless value, 280. 

Premii.un concept of interest, 194- 
196, 247, 334; interchange- 
ability of, with price concept, 
196-199, 362-366; represented 
mathematically and by diagram, 
358-361. 

Price, Richard, financial theories of, 
243. 

Price, definition of, 11, 335; various 
usages of term (money, market, 
and appraised or reasonable), 
13-14 ; distinction between 
quantity, value, and, 14-15 ; 
relation of, to past costs and 
future expectations, 189-190; 
rate of interest called, of money 
or capital, 191 ; money, defined, 
335 ; dimensions of wealth, 
value, and, 341-344. 

Price concept of interest, 191-194, 
196, 247, 334; interchange- 
ability of, with premium concept, 
196-199,362-366; mathematical 
relations between rates reckoned 
annually, semi-annually, etc., 
according to, 357-358. 

Primary (natural) income, 115. 

Principal, nominal, in case of bonds, 
211-212, 215, 217, 335. 

Probability, a matter of human 
estimate, not merely mathe- 
matics, 270-271 ; coefficient of, 
276-277, 331, 335, 403; appli- 
cation of principles of, to valua- 
tion of capital, 277-279, 403- 
406 ; theory of, applied to insur- 
ance, 295. 

Probability computations, 283-284, 
408-410. 



Production, problem of, in con- 
cept of capital, 55-56, 145— 
148 ; cost of, 151, 173-174, 
184. 

Productive processes, 145-148, 335. 

Productive services, 145. 

Productivity, physical and value, 
185-188, 335. 

Productivity theory, 187-188. 

Profits, undivided, 68. 

Promises of refraining, wealth under- 
lying, 27, 28. 

Property, definition of, 18, 325, 335 ; 
rights in, 20-22 ; wealth and, 
correlative terms and coexten- 
sive, 22-23, 95-96; types of 
chief forms of, 26-27 ; partial 
and total rights to, 34-37, 95- 
96, 335 ; necessity of separating 
from wealth, certificates of 
property, services, and utility, 
38 ; confusion of ideas regard- 
ing, 38-40 ; regulation of in- 
come by sale of, 127, 244- 
245. 

Property rights, definition of, 18, 22, 
324, 335 ; table illustrating exist- 
ence of wealth behind, 26-27; 
overlying of, by one another, 31— 
32 ; classification of, 36-37 ; 
method of determining income 
from collection of, 130. See 
Ownership. 

Pseudo-insolvency, 82. 

Psychic income, 167-169, 333; 
measurement of, 177. 

Purchase, definition of, 11, 335. 

Purchasing power, use of phrase, 
191. 

Put, option known as a, 299. 



Q 



Quantity, measurement of wealth in 
units of, 8-9 ; distinction be- 
tween price, value, and, 14-15 ; 
conceived as a fund (capital) 
or a flow (income), 51-52; 
measurement of services by, 120- 
121 ; ratio of, of services to 
quantity of capital yielding those 
services (physical productivity), 
185 ; dimensions of price, value, 
and, 341-344. 

Quarries, terminable income exempli- 
fied by, 209, 210. 



424 



INDEX 



R 



Rae, John, use of economic terms 
by, 5, 65. 

Railway iDonds, source of income 
from, 130. 

Railway capital, fallacious statis- 
tics of, 98. 

Railway control, value of, 35-36. 

Railways, disservices vs. services of, 
120; income accounts of, 138- 
139 ; real sum total of income 
of, 151 ; leases of, as examples 
of perpetual annuities, 208 ; fore- 
casting the value of property in, 
284. 

Rate of capitalization, 194, 330. 
iSee Capitalization. 

Rate of discount, 199, 200, 327-328, 
332. See Discount. 

Rate of flow, 52, 332. See Flow. 

Rate of interest. See Interest, rate 
of. 

Rate of value-return, 229-238. 

Ratios, income-capital, 185-186, 357. 

Raw materials, classification of, 7. 

Ray Act relating to bankruptcy, 83. 

Real estate, regarded as one class of 
wealth, 5 ; classification of, 7 ; 
inaccuracy in appraisement of, 
16-17; speculation in, 221-222, 
254. See Land and Land im- 
provements. 

Real income, concept of, 104-106, 
112-113. 

Realized income vs. earned, 231— 
236, 238, 247-255, 327-328, 
353. 

Real persons, accounting of, dis- 
tinguished from that of fictitious 
persons, 92-93, 138-139, 162- 
164, 174-175. 

Real wages, money-wages not, 104. 

Recapitalization of stock companies, 
70. 

Receiver, office of, in reorganization 
after bankruptcy, 86. 

Rent, as example of transfer of 
wealth, 150-151 ; and cost of 
production, 173-174; spurious 
distinction between interest and, 
186-187. 

Reorganization resulting from bank- 
ruptcy, 86. 

Repair fund, regulation of income 
by, 259-263. 



Repairs, item of, in income and capi- 
tal accounts, 257-263. 

Report on Direct Taxation cited, 114. 

Repudiation of debts, 84. 

Reserves of capital held to avoid 
risk, 290. 

Resources. See Assets. 

Return. See Value return. 

Ricardo, on relation between capital 
and labor, 55 ; theory of rent of, 
187. 

Rider, W., definition of capital by, 
62. 

Right, definition of a, 20. 

Right to subscribe, 78. 

Rights in common, wealth tmder- 
lying, 27. 

Risk, element of, in determining 
capital-value, 205, 210; as 
applied to rate of interest, 271- 
274; as applied to immediate 
income, 275-276 ; coefficient of, 
277, 336; relation between 
amount of capital and, 277, 
408-409 ; five methods of avoid- 
ing, 288 ; avoidance of, by 
method of guaranties, 288-289, 
of safeguards, 289-291 ; safety 
devices for meeting, 290 ; re- 
duction of, by increasing knowl- 
edge, 291 ; avoidance and shift- 
ing of, by insurance, 291-294; 
shifting of, to speculators, 295- 
298; shifting by hedging, 299- 
300 ; effect of element of, on 
capital curves, 320-322 ; mathe- 
matical coefficient of, 403. See 
Chance. 

Risk of insolvency, 81. 

Roosevelt, Theodore, 170. 

Roscher, W., human beings counted 
as wealth by, 5 n.^; treatment 
of capital by, 54 ; definition of 
income by, 346—347. 

Runs on banks, 296, 297. 

S 

Safeguards, method of, to avoid 
risk, 288, 289-291. 

Safety devices, risk-meeting func- 
tion of, 290. 

Sale, definition of, 11, 336. 

Satisfaction, concept of, 41, 324; dis- 
tinction between utility and, 
43-44, 53. 



INDEX 



425 



Savings, to be counted as capital, not 
income, 108, 134-135, 247-253, 
254-255, 328, 349, 353. 

Sawmill, income account for, 152- 
155, 157, 318-320. 

Say, J. B., human beings counted 
as wealth by, 5 n.^ ; use of term 
"capital" by, 60. 

Schafhe, A. E. F., treatment of 
capital by, 54. 

Schmoller, Gustav, on income, 352- 
353. 

Seager, H. R., definition of income 
by, 349. 

Seligman, cited on utility, 47 ; use 
of term "capital" by, 60 n.'. 

"Selling short," 298-300. 

Senior, N. W., quoted on definition 
of capital, 53 ; capital itself 
regarded as a product by, 55 ; 
on capital as a producer of 
wealth, 56. 

Services, definition of, 19, 324, 336 ; 
measurement of, 19-20, 120- 
121 ; complete and partial 
rights to, 36-37 ; to be separated 
from wealth, property, certifi- 
cates of property, and utility, 
38 ; income conceived as flow 
of, 51-52, 101, 116-118, 324; 
commodities wrongly combined 
with, in concept of income, 105- 
106 ; necessity of avoiding con- 
fusion of anything else with, in 
income-concept, 106-107; in- 
finite variety of, 119 ; one phase 
of, and disservices termed "in- 
teractions," 144; transforma- 
tions of wealth as, 146 ; method 
of couples applied to, 152-156 ; 
enjoyable objective ("consump- 
tion"), 164, 165, 336; stage of 
final objective, 165; subjective, 
166; classification of, 178-179. 

Short-time loans, 194-195, 198-199, 
204. 

Simmonds, P. L., definition of 
capital by, 62. 

Single taxation, 253-254. 

Sinking fund, 243-244, 333. 

Smart, William, use of term "capi- 
tal" by, 60 n.'; definition of 
income by, 348-349. 

Smith, Adam, on capital, 53, 54, 
56, 58, 61 ; on rent and income, 
150. 



Social income, the concept of, as "net 
product" of society, 113-115; 
author's concept of, 114, 118, 
141, ^333; distinction between 
individual income and, 115-116. 

Space-units for measuring wealth, 
8-9. 

Speculation, in real estate, 222, 230; 
benefits and evils of, 295-298. 

Speculators, use of land deferred 
by, 222 ; position of, considered, 
230 ; risk-meeting function of, 
288, 290, 295; in futures, 298- 
300. 

Sprague, C. E., cited on meaning of 
term "capital," 63 n. 

Standard deviation, measurement of 
extent of variability by, 406— 
410. 

Standard income, 110, 234, 333; 
vs. realized, 234-236, 247-253, 
327-328, 353. 

Stock, economic use of term, 51, 
336 ; chance element in valuing 
(in commercial sense), 280-283. 

Stock companies, capital accounts 
of, 68-70 ; two valuations in, 
70-72. 

Stockholders, liability of, in joint 
stock companies and in national 
banks, 82-83; preferred, 85; 
bondholders and, contrasted, 
85, 288-289; position of, in 
case of bankruptcy, 85-86; 
risk-taking function of, 288-289. 

Stock jobbing, 74-77. 

Stock of wealth, concept of capital 
as a, 51-52, 323-324. 

Stocks, contrasted with bonds, 85, 
288-289; effect of chance on, 
276-277. 

Stock-watering, 79-80. 

Stream of wealth, concept of income 
as a, 51-52, 323-324. 

Subjective income, definition of, 
168, 326 ; points of divergence of, 
from objective income, 169— 
176. See Psychic income. 

Surplus, 68, 256-257. 



Taussig, F. W., 318; definition of 

income by, 349. 
Taxation: double, 39, 253, 255; 

methods of avoiding double. 



426 



INDEX 



97-98 ; owner-method and 
wealth-method of, 97-98; of 
income, 250-254, 398-403 ; the- 
ory of advocates of single, 254 ; 
of land, 254. 

Taxing power, wealth underlying, 
27; nature of government's, 
30-31. 

Tenant, rights of, 34-35. 

Time, element of : in concept of 
capital, 51-52, 56-57 ; in con- 
sidering interest, 196. 

Todhunter, Ralph, cited, 401. 

Total discount on a sum, 209-210, 
374-378. 

Total social wealth, diagrammatic 
summation of, 316-317. 

Total utility (Total desirability), 
44, 47, 331. 

Trade journals, risk element dimin- 
ished by, 291. 

Transaction, definition of, 159, 336. 

Transfer of wealth, 10-11, 149-152, 
158-159, 325, 336. 

Transformation of services through 
the human body, 167-168. 

Transformations of wealth, defini- 
tion of, 145, 325, 336 ; services or 
disservices according to point 
of view, 146 ; examples of, 147- 
148. 

Transportation of wealth, 148-149, 
325, 336. 

Trust, property held in, 31. 

Turgot, use of term "capital "by, 60. 

Tuttle, definition of wealth by, 4; 
distinction between capital and 
non-capital according to, 55 ; 
use of economic terms by, 60, 67. 



U 



Undesirability, definition of, 42, 336. 

Undesirable event, 123. 

Undivided profits, 68, 256-257. 

Usance of wealth, 117, 348. 

Use of desirable events, "utility" 
to be distinguished from, 19, 43. 

Usufructs, wealth underlying rights 
in, 26. 

Utility, concept of, 19, 41, 42-43; 
to be separated from wealth, 
property, certificate of property, 
and services, 38 ; error of belief 
that wealth constitutes, 39-40; 
distinction between satisfaction 



and, 43-44, 53 ; total and mar- 
ginal, 44, 331 ; consideration of 
marginal, 44-46 ; total, 47 ; 
definition of marginal, expressed 
mathematically, 344-345. 



Valuation of railways, 35-36, 151, 
284. 

Valuations in stock companies 
(bookkeeper's and market's), 
70-72. 

Value, definition of, 13, 336-337; 
varioiis uses of term, and of 
term "price," 13-14; distinc- 
tion between quantity, price, 
and, 14 ; of control in case of 
railways, 35-36 ; measurement 
of services by, 120-121 ; deriva- 
tion of, from future and not from 
past, 188-189 ; riskless, mathe- 
matical, and commercial, 276- 
277, 280-283; dimensions of 
wealth, price, and, 341-344 ; 
increase of, not income, 351 ; 
formula for, of bond, 378-380. 
See Capital-value. 

Value productivity of capital, 185, 
186, 335. 

Value return of capital, 185-186, 
188-191, 202, 336; rate of, 229- 
238 ; may be greater or less than 
rate of interest, 229-231. 

Variation, of income, and its rem- 
edies, 125-129, 243-247, 259- 
263, 293-294; of rate of inter- 
est, 229, 271-273, 284-285, 
390-393, 396-398 ; of dividends, 
281-282, 406-407. 

Verm, theory of chance of, 266. 

W 

Wage fund theory, 59. 

Wages, money, are not real, 104. 

Wagner, Adolf, on income, 125, 
353-354. 

Walker, Francis, 187. 

Walras, human beings counted as 
wealth by, 5 n.^; on capital, 
54, 55-56, 63. 

Waste, an example of overbalancing 
of services by disservices, 120. 

Water-rights, an example of per- 
petual annuity, 193, 208-209. 



INDEX 



427 



Wealth, definition of, in general 
sense, 3-5, 337; "immaterial," 
4, 39 ; classes of, distinguished, 
5 ; definition of, in restricted 
sense, 5-6, 337 ; scheme showing 
classification of, 7 ; measure- 
ment of, 8-17 (see Measure- 
ment of wealth) ; transfer of, 
10-11, 149-152 (see Exchange) ; 
appraisement of, 11-12, 34-36; 
distinction between quantity, 
price, and value of, 14-15 ; 
sources of error in measure- 
ment of, 15-17 ; meaning of 
ownership of, 18 ; services of 
instriiments of, defined, 19; 
rights to services of, 20-22; 
and property correlative terms 
and coextensive, 22-23, 95, 96 ; 
cases in illustration of the corre- 
lation of, and property, 24-36; 
table illustrating existence of, 
behind property rights, 26-27 ; 
partial and total ownership of, 
34-36 ; necessity of separating 
from property, certificates of 
property, services, and utility, 
38 ; division of, into fund and 
flow, i.e. capital and income, 
51-53 ; transformation of, 145- 
148; transportation of, 148- 



149 ; health as, 176 ; appraisal 

of, based on future worth, 204- 

205 ; risk-meeting function of 

stocks of, 290 ; diagrammatic 

summation of total social, 316- 

317 ; dimensions of price, value, 

and, 341-344. 
Wealth-method of taxation, 97-98. 
Wear and tear, depreciation due to, 

210-211. 
Weight-units for measuring wealth, 

8-9. 
Weiss, human beings counted as 

wealth by, 5 n.^. 
Whitman, Walt, 176. 
Wieser, use of phrase "marginal 

utility" by, 46. 
Wine, determination of present 

value of, based on future worth, 

205. 
Wittstein, on human beings as 

wealth, 5 n.^. 
Work, distinction between labor and, 

175 n.2. 
Work dues, wealth underlying, 25, 

26. 



Years' purchase, concept of, 194, 

209, 362. 
Yield, income viewed as, 122 n. 



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